Option Market Liquidity - An empirical study of
option market bid-ask spreads
Master Thesis
ETH Zürich
Chair of Entrepreneurial Risks
Mate Nemes
Supervisors:
Prof. Didier Sornette
Dr. Peter Cauwels
Dr. Mika Kastenholz
December 2012
Abstract
In this thesis we review existing literature on option market liquidity and give
an overview of the current state of research. We also examine the impact of
macroeconomic shocks and low-liquidity market conditions on bid-ask spreads
of stock and ETF options. The core of the paper is a multi-angle analysis of option
bid-ask spreads in times of high liquidity and liquidity squeezes, as well as across
sectors, maturities, and moneyness. The empirical results show rapidly widening
bid-ask spreads as the option sinks deeper into the out-of-the-money space. Large
volatility of spreads and differences between sectors, along with correlation numbers with established fear indices improve general understanding of option market
spreads behavior. Impact of macroeconomic shocks and liquidity conditions in the
market are clearly recognizable on the time series plots of bid-ask spreads. We also
examine options on exchange traded funds to compare and contrast their spreads
with simple equity options. In order to provide a practical guide to estimate how
bid-ask spreads react to changes of exogenous and endogenous variables, we set
up an illustrative regression model.
Keywords:
Options market, liquidity, bid-ask spread, fear index, market maker, regression framework
Acknowledgements
First and foremost, I would like to express my appreciation to my supervisors for their
dedicated help and guidance throughout the preparation of this master thesis. Their insights, ideas, and remarkable knowledge of the topics discussed here, were absolutely
crucial for this work. I would also like to thank Dr. Ryan Woodard for his kind assistance in obtaining option market data. Without his help, it would have been impossible
to perform the analytical tests on real-life market data. In this space, I would also like
to say thank you to all the professors, lecturers, and academic staff for having the privilege to attend their lectures. Moreover, I must thank all my peers at ETH Zürich with
whom I performed project work, group exercises, or simply those who made my days
at ETH Zürich unforgettable.
Contents
1
Introduction
8
2
An overview of the current state of liquidity research
9
3
Liquidity measures
12
4
Option market bid-ask spreads
16
4.1
Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
4.1.1
Order processing cost . . . . . . . . . . . . . . . . . . . . . .
17
4.1.2
Inventory holding cost . . . . . . . . . . . . . . . . . . . . .
17
4.1.3
Model risk . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
4.1.4
Hedging and rebalancing cost . . . . . . . . . . . . . . . . .
19
4.1.5
Other factors . . . . . . . . . . . . . . . . . . . . . . . . . .
20
5
Data and methods
23
5.1
Options data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
5.2
Underlying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
5.3
Examined time periods . . . . . . . . . . . . . . . . . . . . . . . . .
23
5.4
Fear indices and Liquidity proxies . . . . . . . . . . . . . . . . . . .
26
5.4.1
VIX (Bloomberg: VIX Index) . . . . . . . . . . . . . . . . .
26
5.4.2
Ted-Spread (Bloomberg: BASTDSP Index) . . . . . . . . . .
27
5.4.3
US 10-year Treasury yields (Bloomberg: USGG10YR Index .
27
5.4.4
German 10-year government bond yields (Bloomberg: GDBR10
Index) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.5
5.5
28
Italian 2-year government bond yields (Bloomberg: GBTP2YR
Index) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
5.4.6
OTC-X Liquidity Index (Bloomberg: BNKILIQ Index) . . . .
30
5.4.7
Capital Markets Liquidity Index (Bloomberg: CPMKTL Index)
31
5.4.8
Euro-dollar basis swap spread (Bloomberg: EUBSC Index . .
32
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
5.5.1
Time series of average bid-ask spreads . . . . . . . . . . . . .
33
5.5.2
Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
5.5.3
Pinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3
5.5.4
6
Regression model . . . . . . . . . . . . . . . . . . . . . . . .
35
Results
36
6.1
Cross-sectoral analysis . . . . . . . . . . . . . . . . . . . . . . . . .
36
6.1.1
Differences across tenors . . . . . . . . . . . . . . . . . . . .
36
6.1.2
Cross-sectoral differences . . . . . . . . . . . . . . . . . . .
36
6.2
ETFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
6.3
Deep dive: bank sector . . . . . . . . . . . . . . . . . . . . . . . . .
50
6.3.1
High-capitalization vs. low-capitalization banks . . . . . . . .
51
6.3.2
US vs. European banks . . . . . . . . . . . . . . . . . . . . .
56
6.4
Pin risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
6.5
Regression model of bid-ask spreads . . . . . . . . . . . . . . . . . .
63
7
Conclusions
70
8
Outlook
72
A Appendix A
78
B Appendix B
81
C Appendix C
87
4
List of Figures
1
VIX index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2
TED spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3
US 10-year Treasury yields . . . . . . . . . . . . . . . . . . . . . . .
28
4
German 10-year government bond yields . . . . . . . . . . . . . . . .
29
5
Italian 2-year government bond yields . . . . . . . . . . . . . . . . .
30
6
OTC-X Liquidity index . . . . . . . . . . . . . . . . . . . . . . . . .
31
7
Capital Markets Liquidity index . . . . . . . . . . . . . . . . . . . .
32
8
EUR-USD basis swap spread . . . . . . . . . . . . . . . . . . . . . .
33
9
Low-cap cross-sectoral bid-ask spreads in a low-liquidity regime . . .
39
10
Low-cap cross-sectoral bid-ask spreads in a high-liquidity regime . .
39
11
High-cap cross-sectoral bid-ask spreads in a low-liquidity regime . .
40
12
High-cap cross-sectoral bid-ask spreads in a high-liquidity regime . .
40
13
Average bid-ask spreads across various moneyness levels in the Bank
and Technology sectors in the high liquidity regime . . . . . . . . . .
14
Average bid-ask spreads across various moneyness levels in the Bank
and Technology sectors in the low liquidity regime . . . . . . . . . . .
15
47
Tech sector high-cap vs. low-cap average open interest in a high liquidity regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
47
Tech sector high-cap average open interest in a high liquidity vs. low
liquidity regime (x-axis shows a day count for the sake of comparison)
20
46
Tech sector high-cap average trading volume in a high liquidity vs. low
liquidity regime (x-axis shows a day count for the sake of comparison)
19
46
Tech sector high-cap vs. low cap average trading volume in a low
liquidity regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
45
OTM high-cap bid-ask spreads in the tech sector in a low vs. high
liquidity regime (x-axis shows a day count for the sake of comparison)
17
42
OTM high-cap vs. low-cap bid-ask spreads in the tech sector in a low
liquidity regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
42
48
Average bid-ask spreads of options on the most popular ETFs with 1-m
maturity in the low liquidity period . . . . . . . . . . . . . . . . . . .
50
22
Average bid-ask spreads of high-cap US banks in a high-liquidity period 55
23
Average bid-ask spreads of high-cap US banks in a low-liquidity period
5
55
24
Average bid-ask spreads of US banks in a high-liquidity period . . . .
59
25
Average bid-ask spreads of European banks in a high-liquidity period
60
26
Apple OTM option . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
27
Apple ATM option . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
28
Apple ITM option . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
29
Apple OTM vs. ATM vs. ITM in July . . . . . . . . . . . . . . . . . .
63
30
The comparison of the actual and the predicted values for the simple
linear model in the low liquidity period . . . . . . . . . . . . . . . .
31
The comparison of the actual and the predicted values for the simple
linear model in the high liquidity period . . . . . . . . . . . . . . . .
32
34
66
The comparison of the transformed spread and the predicted values for
the final model in the low liquidity period . . . . . . . . . . . . . . .
33
66
70
The comparison of the transformed spread and the predicted values for
the final model in the high liquidity period . . . . . . . . . . . . . . .
70
The output of the Breusch-Pagan test for the simple linear model . . .
87
List of Tables
1
Average relative bid-ask spreads of OTM options (at 90% of the strike
price) across maturities and sectors . . . . . . . . . . . . . . . . . .
2
25th, 50th and 75th percentiles of daily sector spreads distribution in
the high liquidity regime at 90% moneyness . . . . . . . . . . . . . .
3
54
Average bid-ask spreads of high-cap vs. low-cap US banks with 1month maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
53
Correlation of high-cap vs. low-cap banks with the various fear and
liquidity indices at 90% moneyness and with 1-month maturity . . . .
7
53
Correlation of high-cap vs. low-cap banks with the VIX index across
different maturities at 90% moneyness . . . . . . . . . . . . . . . . .
6
38
Correlation of high-cap vs. low-cap banks with the VIX index across
various moneyness levels and with 1-month maturity . . . . . . . . .
5
38
25th, 50th and 75th percentiles of daily sector spreads distribution in
the low liquidity regime at 90% moneyness . . . . . . . . . . . . . . .
4
36
54
Correlation of US vs. European banks with the VIX index across various moneyness levels with 1-month maturity . . . . . . . . . . . . . .
6
58
9
Correlation of US vs. European banks with the VIX index across different maturities at 90% moneyness . . . . . . . . . . . . . . . . . .
10
58
Correlation of US vs. European banks with various fear indices at 90%
moneyness and with 1-month maturity . . . . . . . . . . . . . . . . .
58
11
Average bid-ask spreads of US vs. European banks with 1-m maturity
59
12
The coefficients of the simple linear model . . . . . . . . . . . . . . .
65
13
The ANOVA table of the simple linear model . . . . . . . . . . . . . .
65
14
The normality test of the simple linear model . . . . . . . . . . . . .
67
15
The model summary of the final model . . . . . . . . . . . . . . . . .
68
16
The coefficients of the final model . . . . . . . . . . . . . . . . . . .
69
17
The normality test of the final model . . . . . . . . . . . . . . . . . .
69
18
Average annualized volatility of OTM (at 90% of the strike price) bidask spreads across sectors . . . . . . . . . . . . . . . . . . . . . . .
81
19
Cross-moneyness correlation with the VIX index . . . . . . . . . . . .
82
20
Cross-index correlation of OTM (at 90% of the strike price) bid-ask
spreads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
21
Cross-maturity correlation with the VIX index at 90% moneyness . . .
82
22
Average bid-ask spread, trading volume and open interest across sectors 83
23
Statistical significance of correlation coefficients of the bank sector (pvalues) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
85
Average bid-ask spread of options on the most popular ETFs with 1-m
maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
25
Model summary of the simple linear model . . . . . . . . . . . . . . .
87
26
The residual statistics of the simple linear model . . . . . . . . . . . .
88
7
1
Introduction
Since 15 September 2008, liquidity has been on the forefront of financial markets’ attention. On that day Lehman Brothers, one of the longest standing and most renowned
investment banks, collapsed and its demise triggered a rapid dry-up of liquidity in almost all major markets. Lehman Brothers was deeply rooted in Wall Street’s strong culture and it was unimaginable that such a well-connected and powerful institution could
fail. As Gorton and Metrick (2011) also discussed the topic, the woes that directly
lead to its final collapse started from its prime brokerage division, which conducted
business with hedge funds and other large institutional investors, providing margin
lending, running large scale repo and reverse repo operations, and most of all relying
heavily on short term repo and commercial paper funding. Lehman Brothers, at the
same time, owned large mortgage-backed securities (ABS) portfolios which consisted
mainly of mortgage-backed securities (MBSs), collateral debt obligations (CDOs) and
synthetic CDOs (both are potentially packaged and layered sets of mortgages and other
mortgage backed securities). As the federal housing market started to decline and
house prices behind these assets suffered significant decrease, the homeowners could
not refinance their mortgages, which led to rising delinquency rates on the mortgages
packaged into the aforementioned bonds. Investors started questioning the value of
these assets as well as the firm’s accounting and valuation policy, demanding adequate
write-downs on impacted assets. Concerns grew over time which were, among others,
reflected in collateral requirements on repos. Increasing collateral requirements and
margin calls signaled the growing reluctance to lend to the firm which in turn led to
the complete dry-up of liquidity. This is considered the start of the 2008-2009 financial crisis. Since then, regulators and investors have put large emphasis on addressing
systemic and firm-level liquidity issues. Announcements about large-scale liquidityboosting central bank programs and open market interventions have been dominating
market sentiment around the globe. The Basel 3 framework, developed by the Basel
Committee on Banking Supervision (2011) and is scheduled to start the testing phase in
2013, already includes a Liquidity Coverage Ratio (LCR) which requires banks to hold
sufficient amount of liquid assets that covers the total net cash outflows over a 30-day
period. Banks and large trading institutions started monitoring and partly controlling
liquidity risk, at least on an intraday (operational) level including payment queues, cash
flow forecasts. However, liquidity risk measurement and control have not reached ade8
quate levels and there is plenty of room for improvement. In this thesis, we aim to give
an overview of liquidity in option markets, introduce common liquidity measures and
examine bid-ask spreads, one of the well-known measures, closely. We look at bid-ask
spreads along moneyness and focus specifically on their characteristics for out-of-themoney options. The objective is not to set up a comprehensive guide to liquidity risk
but to give an overview that highlights possible future research topics and looks at option market liquidity from an empirical perspective.
In Section 2, we give an overview of the current state of liquidity research followed
by Section 3 about liquidity measures. Option market bid-ask spreads are introduced
in Section 4. Data and methods used in this paper are described in Section 5 and our
results are presented in Section 6. In Section 7 we conclude our analysis and finish the
paper with an outlook in Section 8.
2
An overview of the current state of liquidity research
Literature on option market liquidity is thin. Most published papers cover currency
options, accessible material on equity options are rather difficult to organize in a clearcut framework. Mayhew et al. (1999), Kalodera and Schlag (2004) and Cao and Wei
(2010) conducted empirical research on individual equity options and published some
of the most frequently cited papers on this topic. Mayhew et al. (1999) found that options are more liquid for stocks with higher price, greater volatility and higher trading
volume. Kalodera and Schlag (2004) examined specifically German stocks and found
that the higher the trading volume of a stock, the higher the frequency and volume of
option trades on the stock. Cao and Wei (2010) examined the overall equity option market and with regard to commonality and other features. They found that commonality
for various liquidity measures is strong even after controlling for the underlying stock
market’s liquidity and volatility. In addition, they also claimed that the market-wide
option liquidity is closely linked to the underlying stock market’s movements and that
information asymmetry plays a more dominant role than inventory risk as a determinant of liquidity.
As similar line of research was conducted by George and Longstaff (1993), who analyzed the bid-ask spread of S&P 100 options in 1989 using various strike prices and
maturities and concluded that the cross-sectional differences are related to costs of mar9
ket makers and frequency of trading. They also found that call and put options behave
as substitutes, their trading volume is dependent upon the ratio of their bid-ask spreads
(if put options have higher bid-ask spreads, trading volumes of call options are higher).
Time series properties of liquidity are only examined by a few researchers. Wei and
Zheng (2010) focused on the trading activity and bid-ask spreads of individual equity options and found that option return volatility (the option elasticity - the absolute
value of the option’s delta - times the stock return volatility) explains bid-ask spread
changes to a much higher extent than previously considered measures such as stock
return volatility and option trading volume. Another finding was the substitution effect
of maturities due to unavailability (market participants tend to trade with the options
that have a maturity closest to the desired one and have sufficient liquidity). Lastly,
the third, rather intuitive, outcome is the moneyness substitution effect described by
the switch to out-of-the-money (OTM) options from in-the-money (ITM)options when
stock return volatility increases, resulting in tightening bid-ask spreads for the OTM
options (in isolation from the increase in volatility).
Chacko et al. (2010) constructed and index-based measure of liquidity, which consists
of long positions in exchange-traded funds (ETF) and short the underlying assets. The
authors observed systematic pricing discrepancies between the ETF and the underlying
assets. They argue that the reason for the pricing discrepancies can be attributed two
things. First, markets are inefficient and the pricing discrepancies represent arbitrages.
Second, the positions differ on liquidity. They assume that systematic arbitrages are
not possible and conclude that, in general, ETFs are more liquid than the individual
components of the ETF. This broadly confirms the common intuition about liquidity of
ETFs.
A rather separate line of research is represented by Bouchaud et al. (2004), who examined the details of prices changes at a trade by trade level and the impact of a series of
individual trades on the price and volatility of stocks. The first finding is that the trades
are almost purely diffusive, the random walk behavior of stock prices also prevails at
the trade by trade level and the diffusion constant is on the order of the average square
of the bid-ask spread. Supported by various examples, Bouchaud et al. (2004) argues
10
that the fluctuation for small tick-size stocks is constant and approximately equals the
tick size, whereas the bid-ask spread is two ticks. Thus, every transaction typically
moves the mid-price by half of the bid-ask spread. Bouchaud et al. (2004) also introduces the market impact factor which shows how much the price increases in average
over time after an initial buy order, depending on a power-law function of the volume
of the trade:
R(T, v) = E[(pT − p0 )0 |v0 = v]
R(T = ∆t, v) α v ψ(∆t) ;
ψ(∆t) ≤ 1,
where v is the volume; ∆t is the elementary time scale, ranging from the average transaction time to hours or days; p is the price at the respective point in time; and ψ is an
exponent increasing with the elementary time scale, taking rather small values for individual trades and increasing towards 1 when ∆t corresponds to several thousands of
trades.
The second important result based on this is that the temporal structure of the impact
function first increases up to a maximum after 100-1000 trades, and then starts to decrease with a rather limited variation. Third, as Bouchaud et al. (2004) put it, ”the
sign of the trades shows surprisingly long-range (power-law) correlations, at least up
to 15000 trades (two trading days)”.
A recent interesting empirical finding is the role of high-frequency trading in market
liquidity and how it revealed the fundamental differences between volume and liquidity. As discussed by Lauricella (2010) and The Technical Committee of the International Organization of Securities Commissions (2011), high-frequency trading played
a pivotal role in the flash crash on 6 May 2010. Typically, HFT algorithms submit thousands of orders with low volumes in a matter of seconds (and often also revoke them)
and thereby deceiving the market with the perception of high liquidity. However, in reality, HFTs are willing to provide these volumes in normal and usually slightly trending
market conditions but only in very small lots. In other words, the depth of the quotes
and the depth of the HFT-dominated markets are very low and even this level of liquidity is dependent on other factors. HFTs withdraw liquidity from the market in a
split second if they detect any unusual activity or pattern. This means that in a severe
11
downturn or in a situation when markets need liquidity, HFTs do the exact opposite
and take away liquidity. These algorithms also often account for a significant portion
of the total trading volumes. If the algorithm shuts down, a large volume will be taken
away from the market which amplifies the liquidity problems, creates further swings,
and prevents other market participants from trading, damaging the whole market.
3
Liquidity measures
In order to examine liquidity in option markets, we require adequate ways and proxies to measure it, which can be implemented without excessive computational or data
requirements. There are various measures of liquidity in option markets in academic
literature. However, some of these measures do not match the practitioner’s view of liquidity and often provide counter intuitive or conflicting results. In this space, only the
most important and commonly accepted measures are discussed without the intention
to provide a complete list of available ones. We rely mainly on Cao and Wei (2010) for
the list of measures below:
• Contract volume, defined as the total number of options traded during the day.
• Dollar Trading volume: the midpoint of the bid and ask quotes times the volume
summed over all the options within the day.
• Trading volume represents the number of shares traded in a certain time period.
It can be calculated for various intervals, starting from yearly turnover down
to daily granularity. Trading volume inherently shows a high correlation with
issued or outstanding amount for all securities, therefore it should only be used
with awareness and as a complementary measure.
• Turnover is equal to the product of the volume and the price of the same transaction summed up during a specific time period. Turnover makes comparison between different securities of the same type possible and serves as a better proxy
for liquidity. However, it is often used in a relative form to further correct for
differences across securities in a certain market.
• Relative turnover is simply the absolute turnover described above, normalized
with the number of shares outstanding, floating free on an exchange. Regarding liquidity, relative turnover provides a more accurate picture augmented by a
12
capitalization weighting. This relative turnover as described by Sarr and Lybek
(2002), shows how many times securities change hands. Relative turnover is using the same analogy as the velocity of money, as also mentioned by Sarr and
Lybek (2002).
• Sarr and Lybek (2002) suggested another measure; although mostly used in
academic research only, where they combined two additional liquidity measures:
the market index average daily price change and the ratio of the market index
daily price change and turnover rate.
The market index average daily price change is closely related to the market-level
volatility. A lower level would indicate a higher liquidity. By their logic, a higher
price change suggests lower liquidity. The ratio of the market index average daily
price change and the turnover rate represents the effect of turnover and market
capitalization on index volatility. The higher the ratio, the lower the liquidity and
possibly the lower the depth due to the greater impact of large transactions on
the price and the lack of high-volume transactions with tight spreads.
• Quote/Market depth tells us the number of option contracts for which the quote
is valid. Low number of ask prices, relative to previous prices, might only be
valid for a significantly lower number of available options, meaning the depth of
the quote is rather low. According to common practice, a higher market depth
contributes to higher liquidity. Market depth is defined as the size threshold of a
trade necessary to move the market a given amount.
• Frequency of trades tells us how many times securities change owners in a time
interval. Alternatively, the time between two consecutive trades can be measured, in order to express how often transactions occur. In isolation, higher frequency figures are commonly, although often falsely, assumed to indicate higher
liquidity. Higher readings of the time between two consecutive transactions suggest lower liquidity; however, this is certainly not sufficient for determining liquidity. Number of orders is also commonly used instead of number of transactions during a certain period of time. Number of transactions in an interval is
used by practitioners for comparison between various markets. The difference
between the frequency of trades and relative turnover is that the latter uses free
float as the correction, while the former considers the trades only. This means
13
that the two measures are certainly not the same (simply turnover is a ”dollar
amount”, while frequency is the reciprocal of time between trades). An interesting point here is the impact high frequency traders (HFT) have on the market.
These traders post hundreds, thousands, or even higher number of orders per
minute, often also execute trades with a very high frequency. This gives the impression of high liquidity in the market. However, these high frequency orders
have little depth, often only one or a few units. This can certainly not be considered high liquidity as trades with higher amounts will not be executed on these
prices or will not be executed at all. HFTs are often built on trend-following
strategies (i.e. scalping or skimming) which generate volume but reduce liquidity or on liquidity-making strategies which utilize liquidity rebates offered by
exchanges for providing securities for trade when needed in reality but do not
provide real liquidity due to negligible quote depths.
• Open interest means the total number of option contracts currently open. According to Graham (2012), these are the contracts that have been traded but not
liquidated yet by an exercise or by an offsetting trade. Note that open interest is
not the same measure as trading volume. If a trader buys 10 calls on a particular
stock, buying the calls to open, it adds 10 to the open interest. When the trader
sells these options to close, open interest falls by 10. Selling options can also
add to open interest if the trade is a sale to open transaction. For example, the
trader owns sufficient number of shares of a particular company and intends to
do a covered call by selling 10 call options. This adds 10 to the open interest
again. If the trader later repurchased the options (buy to close), open interest
would decrease by 10. In case the options traded in a transaction are not created by the same transaction, calculation is more complicated. If a trader sold
10 calls to open but the other side of the trade was taken by someone who buys
to close, the overall open interest number would not change. From a liquidity
perspective, open interest is a very informative measure. If the open interest for
an option is low or zero, there is no secondary market for that option. The higher
the open interest, the easier it is to get orders filled at fair prices and trade the
option with relatively small bid-ask spread (bid-ask spreads are discussed in Section 4). Open interest is also interesting relative to the volume traded. Graham
(2012) points out that if the daily trading volume is higher than the open interest
14
on a particular day, trading activity is considered exceptionally high that day.
• Liquidity ratio 1: As Franić (2008) describes it:
LR1t =
T nt
=
|rt |
PN
pi × qi
|rt |
i=1
where LR1t denotes liquidity ratio over time ∆t, pi is the price, qi is the amount
traded, rt is the return (the percentage price change as the absolute value). The
liquidity ratio 1 expresses the turnover in terms of absolute price change in a
time interval. The liquidity ratio 1 is often referred to as Amivest ratio (named
after the company, which created it). Larger price changes can be absorbed if the
turnover is higher. Of course, high liquidity ratio 1 means higher liquidity. In
case the return is zero, LR1t resets to zero.
• ILLIQ: the ratio of stock return to its dollar volume, averaged over a certain time
period, introduced by Amihud (2002). Calculated daily, it describes the daily
price response associated with one dollar of trading volume, thus as Amihud
(2002) puts it, serving as a rough measure of price impact. The generally used
formula for the monthly ratio is the following:
i
Dayst
X Rtd i
1
i
×
ILLIQt =
×
,
i
Dayst
Vtd i
d=1
where R is daily return, V is daily volatility, t denotes the time period, d refers
to days and t to months. ILLIQ is also simply the reciprocal of LR1:
ILLIQit =
1
|rt |
=
.
LR1t
T nt
There are two versions of ILLIQ used in literature: AILLIQ or the absolute
change in daily closing price divided by the dollar volume and PILLIQ or the
percentage change in daily closing price divided by the dollar volume. Franić
(2008) argue that for options, the AILLIQ and PILLIQ measures are constructed
similarly with two important modifications. First, the daily change in option
prices is adjusted by the product of the option’s cash delta and the cash change in
the underlying stock price. This adjustment accounts for the change of the option
price solely due to the change in the underlying security price. Second, a volume
15
weighted average is calculated for each measure using the trading volume of
each option.
• Probability of Informed Trading (PIN) is also used as a liquidity measure, as
trading against adverse information is often by far the most heavily-weighted
component of the bid-ask spread. Informed trading might come from illegal
insider information or better analysis of publicly available data. PIN is therefore widely used as a quantitative measure, based on the Poisson distribution.
PIN was introduced by Easley et al. (1996) and suggested an empirical method
that allows to estimate the probability of informed trading and that has subsequently been used to address a wide range of issues in market microstructure.
PIN was originally decomposed from the adverse selection component of the
bid-ask spread. As Grammig and Theissen (2003) puts it, the data needed for
estimation is the number of buyer- and seller-initiated trades.
4
Option market bid-ask spreads
In general, the price at which an investor can sell (buy) is lower (higher) than the
value of the asset. The difference between the selling price (bid price) and the buying price (ask price) constitutes a bid-ask spread, which reflects the transaction costs
of trading. It provides an approximate cost of trading, mostly for market makers and
dealers. Traders pay clearing and/or transaction fees to the option or stock exchange
and brokers, which are calculated for each individual transaction. Bid-ask spreads
also compensate dealers for providing immediacy service (the costs convenience of
trading without significant delay) and for taking the model risk (especially for out-ofthe-money options). Narrow bid-ask spreads indicate high liquidity. The most simple
version of bid-ask spread is the absolute or quoted spread, calculated as the difference between the lowest ask price and highest bid price. Absolute spreads are always
positive and their lowest value is the tick size. There are numerous types of bid-ask
spread measures such as log absolute spread, relative spread, effective spread, as in
Roll (2012).
4.1
Composition
As opposed to the three components of the bid-ask spread in the cash market (order
processing cost, inventory holding cost, and trading against adverse information), the
16
bid-ask spread of traded options is determined by four main factors. As Chan and
Chung (1999), George and Longstaff (1993), and Engle and Neri (2010) explain, the
following factors directly influence the bid-ask spread:
• Order processing cost;
• Inventory holding cost;
• Model risk;
• Hedging and rebalancing cost;
The components and their impact are described below.
4.1.1
Order processing cost
The order processing cost includes the transaction costs, clearing fees, costs of market
making, infrastructure and labor expenses, costs of providing quotes at all times, as explained by Demsetz (1968). These are mainly fixed costs, although higher transaction
volumes reduce per-trade effects of these factors. Kim and Murphy (2011) explain that
the fixed transaction cost will always be incurred and additional costs will be incurred
for large trades because the supply schedule has an upward slope reflecting how large
orders climb up in the order book.
4.1.2
Inventory holding cost
Market makers have to carry an inventory of options available for trade any time. This
implies rebalancing costs to prevent imbalanced inventories, i.e. the risk-related costs
of carrying the inventory. The funds locked up in the inventory also imply opportunity
costs, which is equal to the missed returns of investments in other asset classes or
assets. Literature on inventory holding costs is extensive and considered complete
( Tinic (1972), Huang and Stoll (1997), Amihud and Mendelson (1980), Ho and Stoll
(1981)). Stoll (2012) argues that inventory holding costs increase with the opportunity
costs of holding a tradable portfolio. This implies that lower funding costs, ceteris
paribus, lead to lower inventory holding costs reflected in narrower spreads.
4.1.3
Model risk
Model risk comes from the inappropriate choice of option pricing models or the parameters of those. Higher than expected stochastic volatility or tail-events can easily
17
cause inaccurate pricing of derivatives regardless of the pricing model. Scotti (2012)
performed a thorough analysis on the effect of parameter uncertainty on a stochastic
volatility model and showed that his analysis can justify endogenously the presence
of a bid-ask spread on the option prices. Important to note that this component is
particularly pronounced for OTM options, given that tail-risk influences this space in
moneyness. In case of ITM options, the uncertainty is less relevant. There is no downside and trading in these options is limited as the underlying can be purchased with
lower costs due to tighter bid-ask spread.
Routledge and Zin (2009) explain that the pricing model is built on limited and imperfect data, mostly in terms of volatility. Market makers and dealers typically stress
test their models to obtain a realistic picture of adverse outcomes and an approximate
shape of the distribution. Still, how large the tail should be and what distribution to
use remain key questions. Bid-ask spreads can be used to compensate for this uncertainty based on the outcomes of the stress test. Routledge and Zin (2009) describe
the model risk component the following way: ”When there is ambiguity about the appropriate probability distribution of future cash-flows for the underlying security, the
market maker is uncertain about the dynamic consequences of their derivatives trading.
This uncertainty increases the market-maker’s bid-ask spreads and reduces liquidity.”
Scotti (2012) proposed a method to transfer uncertainties of the option prices in a basket into the uncertainty around the calibrated parameters of market maker, which he
considered monopolist for the sake of simplicity in his analysis. First the calibration
is performed with neglecting the bid-ask spread and with fixing the option price at the
mid-price. Then an option j is fixed on the basket used to calibrate, its price is shifted
to ask price and then re-calibrated. The new calibrated parameters then represent a
stress of the previously calibrated parameters. Afterwards, Scotti (2012) calculated the
difference between the two set of parameters and interpreted it as standard deviation
of calibrated parameters, which are submitted to a stress into the price of option j. He
was then able to reconstruct the variance-covariance matrix with respect to the random
source in option j. The process was then performed for all options in the basket and,
as the final step, the global variance-covariance matrix was constructed.
18
The issues and costs associated with model risk are amplified by the presence of informed traders. The risks stem from trading in an environment characterized by asymmetric information as laid out by Bagehot (1971), Glosten and Milgrom (1985), Kyle
(1985), Amihud and Mendelson (1986), Easley and O’hara (1987), Glosten and Harris
(1988), and Admati and Pfleiderer (1988). As Black (1975) discussed it, informed market participants prefer trading in options due to higher leverage and/or lower upfront
costs, although transaction fees might be higher.
4.1.4
Hedging and rebalancing cost
On top of the three types of costs described above, the market maker in the option
market also have to face the cost of hedging and rebalancing his portfolio. Cho and
Engle (1999) show that the inventory of options in the market maker’s trading book
is essentially a derivative portfolio, which requires delta hedging with the underlying
securities. They state that the hedging cost is therefore proportional to the percentage
delta:
∆% =
∂ct St
·
∂St ct
where ct is the option price while St is the price of the underlying security.
However, as Kaul et al. (2004) argue, that rebalancing the initial hedge incurs additional
rebalancing costs, proportional to vega (shows how much the option’s price changes
for a 1 percentage point change in the underlying’s volatility) times the spread of the
underlying security.
Other proxies to the rebalancing costs are also often used: Petrella (2006), for example,
models these costs with gamma times the variance of the underlying security:
∂ 2 ct
· (dSt )2 ,
∂St2
where the first term is gamma (Γ) and the second term corresponds to the variance of
the underlying. As Engle and Neri (2010) put it, this captures the second order term of
the options inventory value as market moves, while the first order term is captured by
the initial hedging cost, as introduced by Cho and Engle (1999).
19
4.1.5
Other factors
The magnitude of the listed effects depend on various other measures, such as the
moneyness, the delta of the particular call or put, transaction and clearing costs, and
price volatility caused by new or adverse information.
Chaudhury (2011) discovered that the option volatility surface might introduce substantial bias into spread measures, thus relative percentage spreads might suggest liquidity levels which are contradicting the general view and lead to false conclusions. Chaudhury (2011) introduced alternative measures which are scaled by implied volatility.
The first one is the Spread Relative to Dollar Volatility (SRDV):
SRDV =
100 ∗ DS
,
DDV
where DS is the dollar spread and DDV is the daily dollar volatility of the asset. Here
DDV is derived the following way:
DDV = S × σi ×
p
1/252
where S is the underlying asset price and σi is the annual implied volatility (from the
moneyness).
Chaudhury (2011) argues that the new measures do not introduce any bias in the liquidity measure due to the relative levels of the option prices. However, the volatility
smile might still decrease the SRDV’s adequacy as a liquidity measure but this can
be prevented by including a multiplier in the calculation based on the ratio of average
volatility of the option bucket and the average volatility of ATM options.
The second one is the Implied Volatility Relative Spread (IVRS):
IV RS = 100 ×
(σiA − σiB )
,
σiM
where σiA is the implied volatility of the ask price, σiB is the implied volatility of
the bid price and σiM is the implied volatility of the mid price. IVRS resembles the
conventional relative spread with the difference that the bid, ask, and mid prices are
expressed in implied volatility units.
Besides the four components introduced above, there are also other market and external factors which influence the bid-ask spread of traded options. The characteristics of
20
the order book also play a large role in determining actual bid-ask spreads for particular trades. The best bid and ask prices are valid only for a certain amount of options.
In case of a large trade, a chunk of the trade will be executed at the best ask and the
second chunk will be fulfilled at a higher price, and this goes on until the whole order
is filled (if it is filled at all). This shows how large trades climb up the order book. The
mechanism is similar for the bid price. After the best bid price is hit, the seller typically
shifts the bid price lower. This process widens the bid-ask spread, although most of the
time only temporarily.
As such, the microstructure of the market has a rather large impact on the bid-ask
spreads. The tick size, the number of market makers, transaction costs, transparency
and disclosure rules all belong to these factors. There were two interesting phenomena
in recent years that serve as an example of how changes in the microstructure result in
changes of the bid-ask spread.
The first one is the decimalization of option market quotes in 2007 which reduced the
tick size of exchange traded options. As a recent International Securities Exchange
(2011) analysis explains, before 2007, options were quoted with MPVs (minimum
price variations) of $0.05 for premiums below $3.00 and $0.10 for premiums above
$3.00. In 2007, the SEC launched a pilot program on six option exchanges, called the
Penny Pilot Program. Within the framework of the program, MPVs were set to $0.01
for premiums below $3.00 and to $0.05 for premiums above $3.00. ETFs were already
traded in penny ($0.01) increments by this time. This kind of structure certainly leads
to a jump in relative bid-ask spreads for premiums close to $3.00.
Bid-ask spreads tightened after the decimalization but the quote depth decreased significantly. According to Bangia et al. (2002), quote depth is defined as the volume of
shares available at the market maker’s quoted price. Several studies on the decimalization concluded that in general the reduction of tick size led to higher liquidity. However,
there were also adverse effects of the penny pilot program, especially regarding institutional traders. Rhoads (2011) pointed out that the number of contracts on both sides
of the quotes decreased substantially in several cases, which proved to be an obstacle
to institutional traders executing their full orders at the bid or ask price. Rhoads (2011),
on the other hand, admits that the impact to individual traders has been positive because
21
the cost of entering and exiting positions was reduced.
Another example is the steeply increasing activity of high frequency traders (HFTs),
which carve out significant shares of all trades and orders in option markets. HFTs are
(often falsely) considered beneficial from an overall liquidity perspective because by
posting thousands of orders per minute and executing larger number of trades than other
participants, they contribute to the liquidity of the market and to narrower spreads, at
least according to the general (poorly informed) view. On the other hand, a few of the
HFT strategies cause the bid-ask spread to move to the opposite direction. These HFT
strategies often involve the so-called ”front running” technique. An example for this is
presented by Arnuk and Saluzzi (2009) when they discuss the latency-arbitrage strategy. HFTs subscribe to live data feeds of exchanges and thus immediately (and earlier
than others) see large orders on the tape or detect them using flash orders (if possible),
consisting of the submission and lightening-fast cancellation of orders. Important to
note that flash orders are not allowed in some exchanges any more. If the algorithm
discovers a large block order in the order book, it submits buy orders to hit all the existing quotes at the current level. Subsequently, using its infrastructural advantages, it
resubmits offers a tick or two higher and fills the order of the institutional trader. With
this, the HFT can earn up to a cent or two on every security sold, thereby making the
institutional or block trader worse off. This mechanisms effectively widens the spread
for the rest of market participants. The hidden orders and hidden spreads make it more
difficult for market makers to manage their risks in a fast-enough manner and lead to
permanently higher bid-ask spreads. As a recent Bank for International Settlements
(2011) study discusses, the size of the bid-ask spread is not the only determinant of
liquidity. The size, which determines quote depth, and the lifetime, which indicates
how long the quote stays in the market before it is cancelled, are also important factors
in overall liquidity. HFTs with certain strategies often provide relatively low bid-ask
spreads; however, the quality (mostly in terms of depth and persistence) of these are
not comparable to those of conventional market makers.
According to Engle and Neri (2010), various options markets also influence the microstructure of one another. As Mayhew (2002) argues, options listed on multiple exchanges trade with narrower spreads than those listed only on a single exchange. May-
22
hew (2002) also observes that spreads become wider as soon as one of the multiple
exchanges delists the option.
5
5.1
Data and methods
Options data
For the analysis, Strickland & Associates’ End of Day Options Data from Stricknet.com (2012) was used which consists of all traded options in the United States
and Canada. The daily closing data includes the type of the option, the strike price,
the maturity date, the last price, the bid price, the ask price, the volume traded, and the
open interest. The underlying for these options are exchange traded shares of US-listed
companies and exchange traded funds (ETFs). ETFs include currencies, equities, commodities, indices, and generally all available underlying assets. Options were available
for all maturity dates and strike prices. Important to note that the dataset only includes
the US listed options of foreign companies. Over 400,000 US-listed options are included in the database which thus requires careful selection and filtering. Data was
obtained for the time period from 1 January 2011 to 31 July 2012. The database only
contains the maturity year of options before October 2010, the exact maturity date is
not available.
5.2
Underlying
Underlying assets include exchange traded shares of public companies and ETFs. For
each particular underlying, daily opening and closing, as well as the highest and lowest
prices and daily trading volume were available. The data includes over 30,000 USlisted stocks and ETFs.
5.3
Examined time periods
The available data covers a particularly eventful and challenging time period for global
economies and financial markets. The time period starting on 1 January 2011 followed
a bullish period on global equity and commodity markets with major US, European
and Asian indices exhibiting large gains during the recovery process from the shock
caused by the subprime credit crisis in 2008. The escalating European sovereign debt
crisis, the slowing growth in the Asia-Pacific region, and the subdued US recovery
all posed formidable challenges for financial markets. Governments and central banks
23
have played an increasingly important role through interventions and changing regulation.
In the US, the Federal Reserve (Fed) launched the second round of quantitative easing,
commonly referred to as QE2 (from November 2010 to June 2011), by purchasing treasury securities, which increased the monetary base. The aim of all quantitative easing
programs was to stabilize markets, boost liquidity and stimulate the economy. Quantitative easing aims to inject a predetermined quantity of money into the economy. This
money is created by the central bank for this purpose. While in QE1 the Fed targeted
mortgage bonds (MBS products), this time they purchased mainly treasury securities
($600 billion), government bonds, from banks and market participants, therefore decreasing short-term interest rates and lowering yields, essentially steepening the yield
curve. Quantitative easing, by design, leads to higher excess reserves for banks and
higher asset prices. This certainly has an inflation-supporting impact to maintain inflation around or above the target level to avoid deflation. Along these lines, the Fed
also launched its Operation Twist aiming to flatten the yield curve when already low
short-term interest rates did not allow for further monetary loosening. The objective of
Operation Twist was lowering long term interest rates by purchasing long-dated and,
at the same time, selling short-dated government bonds, thus ”twisting” the yield curve.
In the UK, the Bank of England also pursued its own quantitative easing through asset
purchases, mostly UK government debt (gilts). The Monetary Policy Committee have
expanded the quantitative easing several times since the launch in 2009 and kept its
benchmark lending rate low. The Bank of Japan and several central banks undertook
the same approach.
In Europe, the European Central Bank (ECB) maintained record low interest rates
(1.5% until 9 November 2011, then1.25%until 14 December 2011 and 1% onwards until the 0.25% rate cut on 11 July 2012) and performed several open market operations.
The ECB purchased covered bonds several times as well as European government debt
to expand the monetary base, boost liquidity, lower interest rates generally and also
specifically yields on certain countries’ government debt (mostly of those severely impacted by the European debt crisis). The central bank also launched 12-month and
24
36-month long term refinancing operations (LTROs). The LTROs provided banks with
long term loans with low interests rates backed by an extended set of collaterals (lower
rated asset backed securities and performing credit claims, i.e. bank loans, are now
accepted).
The policies and interventions described above all aimed, together with other goals, to
boost liquidity in financial markets. The vast majority of the current analysis was performed on two distinct low and high liquidity time intervals. The low liquidity period
is characterized by high volatility and downward trending trading volumes, while the
high liquidity period is described by low volatility and stable, slightly increasing trading volumes. The low liquidity interval spanned from 1 August 2011 to 26 September
2011. This period started with the downgrade of the US long-term credit rating from
AAA to AA by Standard and Poor’s. The downgrade had several types of impact
from the financial markets’ perspective. Collateral requirements on derivatives and
structured products necessitate higher collateral posted in the form of US government
bonds. This reduces liquidity of widely interconnected banks trading with structured
products (often relying on US and other high-rated treasury securities as collateral).
The downgrade also triggered high uncertainty in all markets, showing a general loss of
confidence. More importantly, the Greek debt crisis escalated by this time with Greek
credit default swap (CDS) spreads reaching all time highs. CDS spreads are regarded
by markets as a way to price credit risk; rising spreads suggest increasing risk. From
end of August, Greek CDS spreads have stayed above 2000 basis points and kept rising.
The high liquidity interval taken here started on 1 February 2012 and ended on 29
March 2012. After the joint action of 8 central banks to cut US dollar borrowing
rates at the end of November, another major intervention came in December. On 21
December 2011, the ECB launched the first LTRO which succeeded in boosting liquidity in global markets. Volatility started to decline, trading volumes increased, and
major indices started rising within a few weeks. Overnight deposits at the ECB and
the overnight indexed swap (OIS) rates along with LIBOR-OIS spread also decreased,
which together suggest increased interbank lending. The second LTRO was launched
on 29 February 2012 which amplified these trends supported the market rally in the
first few months of 2012. During this high liquidity period, volatility indices such as
25
the VIX and the MOVE (we introduce both indices in Section 5.4) sank below threshold levels regarded as the boundary for high and low liquidity (e.g. VIX sank below
20). The LTRO was supported by other macroeconomic events, such as the Greek debt
restructuring on 9 March 2012 and positive US employment data releases.
5.4
Fear indices and Liquidity proxies
In this subsection, we list fear indices and liquidity proxies used in our analysis to
calculate correlation with. These are widely regarded as relatively accurate indicators
of liquidity in the respective markets or often even globally. Correlation is calculated
between the daily return time series of the average bid-ask spreads and the daily return
time-series of the respective fear index.
5.4.1
VIX (Bloomberg: VIX Index)
The Chicago Board Option Exchange Volatility Index (VIX) is regarded as the most
important ”fear index”. Rising VIX indicates rising volatility and declining liquidity.
The VIX (Figure 1) is quoted in percentage points and reflects the market risk-neutral
expectation for the S&P 500 return volatility over the next 30 days.
Figure 1: VIX index
26
5.4.2
Ted-Spread (Bloomberg: BASTDSP Index)
The Ted-Spread (Figure 2) is the difference between the 3-month London Interbank
Offered Rate (LIBOR) and 3-month US treasury yields in basis points (bps). The name
Ted comes from the concatenation of T-bills and EDs (the ticker for Eurodollar future
contracts represented by the LIBOR). The Ted-Spread is calculated also for other tenors
but the widely used one is the 3-month spread. Rising Ted-Spread usually suggests a
downturn in US stock markets and a dry-up of liquidity.
Figure 2: TED spread
5.4.3
US 10-year Treasury yields (Bloomberg: USGG10YR Index
US 10-year Treasury notes (Figure 3) are commonly considered one of the safest assets
available in the market due to the perceived credit quality of the United States. In
times of market turbulence or crisis, investors allocate more funds into Treasury notes
and lower the yield on those. Often they are referred to as safe haven assets, along
with certain other assets such as German (see below) and UK treasury securities, as
well as gold. Historically, relatively low yields characterized low liquidity and high
volatility regimes, while the opposite was true for high liquidity and low volatility
periods. Interestingly, the downgrade of the US long term credit rating did not change
27
the T-notes’ safe haven status and yields even shrank after the downgrade. This is
commonly referred to as flight to safety. Since then, consistently low yields can be
witnessed; however, this can also partly be attributed to the Fed’s Operation Twist.
Figure 3: US 10-year Treasury yields
5.4.4
German 10-year government bond yields (Bloomberg: GDBR10 Index)
German 10-year government bonds (Figure 4) are the choice of risk averse investors
and asset managers in the Euro area or those who are seeking low-risk exposure to
the Euro zone. The German government’s credit quality is still among the few AAArated ones, the highest possible. Yields on German government debt (bunds) followed
a similar trajectory to that of the US treasury yields, i.e. declining since the beginning
of the European debt crisis. Changing liquidity conditions can be observed through the
oscillations of the bund yields. Low levels appear to be persistent on a longer term but
changes and disturbances still suggest drops and spikes in market liquidity.
28
Figure 4: German 10-year government bond yields
5.4.5
Italian 2-year government bond yields (Bloomberg: GBTP2YR Index)
Since 2011, when Italian budget deficit issues appeared in the forefront of Euro-zone
politics and media, Italian 2-year government bond yields (Figure 5) have been considered an accurate fear index. Rising yields usually signal declining liquidity and
deteriorating market conditions. Above 7% yields, the debt trajectory of the country
is deemed unsustainable, as indicated by Antonucci and Lin (2011). Yields on Spanish government bonds have behaved in a similar manner in the last two years, closely
following developments of Euro-zone rescue plans, bailout proposals and decisions (or
the lack of them) in G-8 and G-20 meetings. After preliminary analysis, we found that
Italian bond yields followed Euro-zone events more closely than Spanish bond yields.
In recent times, demand for 10-year Italian bonds collapsed to almost zero, while demand for 5-year bonds dropped significantly due to the country’s mid-term prospects.
29
Figure 5: Italian 2-year government bond yields
5.4.6
OTC-X Liquidity Index (Bloomberg: BNKILIQ Index)
Based on discussions with Zürich-based cash equity traders, we have included the
OTC-X Liquidity Index (Figure 6) in this thesis to account for latent or hidden liquidity in OTC markets. The OTC-X Liquidity Index is an equally weighted equity
index and contains the 100 most liquid shares in the Swiss market. The index is calculated using bid prices. Important to note, that the index is not directly related to the
liquidity of exchange-traded securities; it only allows to monitor changes on the OTCX platform. However, it might be interesting to take a look at its correlation with the
examined spreads and other liquidity proxies.
30
Figure 6: OTC-X Liquidity index
5.4.7
Capital Markets Liquidity Index (Bloomberg: CPMKTL Index)
According to its fact sheet, provided by the Dorchester Capital Management Company (2008), the Capital Markets Liquidity Index is calculated from the the total return
of over 98% of the traditional investment grade U.S. liquidity markets. The components include investment grade fixed income securities with maturity dates within one
year issued by the U.S. Treasury, U.S. federal agencies and other U.S. governmentsponsored entities, as well as U.S. corporations. The index also incorporates money
market instruments including: commercial paper, bankers’ acceptances, U.S. federal
agency discount notes and certificates of deposit. The Capital Markets Liquidity Index
can be seen in Figure 7.
31
Figure 7: Capital Markets Liquidity index
5.4.8
Euro-dollar basis swap spread (Bloomberg: EUBSC Index
The euro-dollar basis swap (Figure 8) is a cross-currency basis swap agreement in
which one party borrows from the other party in one currency and at the same time
lends the same value in another currency (floating rate to floating rate). The first party
regularly (i.e. per three months) pays for the borrowed amount an agreed interest rate
plus the spread of the basis swap and receives the agreed interest rate for the funds
borrowed. At the end of the term, the difference is paid, as no principal exchange takes
place. The euro-dollar basis swap exchanges floating rate euro-denominated financial instruments for floating rate dollar-denominated financial instruments. The spread
shows the effective price for exchanging these instruments. In times of financial turmoil, the spread tends to increase which suggests dollar chasing or flight to safety. It
represents a funding squeeze of banks from the euro funded block relative to the dollar
funded block.
32
Figure 8: EUR-USD basis swap spread
5.5
Methods
5.5.1
Time series of average bid-ask spreads
Daily average bid-ask spreads were taken for the groups of high and low capitalization companies selected from the upper 10 percentile and lower 10 percentile of the
Yahoo Finance sector classification (see Appendix A). Altogether, the analyses were
performed with 8 sectors for the above-mentioned high and low liquidity regimes (tables can be found in the Results section). This time, only call options were considered
in order to compare the same type of securities. As the put-call parity implies that
puts and calls can be used interchangeably in any delta-neutral portfolio, examining
only calls does not limit the application of findings to call options only. Note that the
put-call parity is valid for European put and call options with identical strike prices
and maturity dates but it can be rearranged into an inequality for American options to
obtain upper and lower bounds for the price, as discussed in Bemis (2006). Options
with a bid/ask price of 0 were excluded from the analysis. Tenors considered for the
analyses were also selected based on pre-defined rules. All US options are assigned
into one of three categories: January cycle, February cycle, and March cycle (the name
refers to the first expiration month in the calendar year). Each cycle has expiration
33
months one quarter apart (i.e. January, April, July, October). Due to the quote and
listing conventions on US exchanges, the following group of tenors were used:
• Maturity in the current month or the following month (referred to as 1-month
options later)
• Maturity in the third or the fourth month (referred to as 3-month options later)
• Maturity in the sixth or the seventh month (referred to as 6-month options later)
Throughout the paper, relative bid-ask spreads were used which equal the absolute bidask spread divided by the mid-price.
RBAS =
P A − PB
,
PM
where RBAS is the relative bid-ask spread, PA is the ask price, PB is the bid price
and PM is the mid price. Moneyness was calculated as the %-ratio of the current price
to the strike price of the underlying:
M% =
PM
· 100%,
PS
where M is the moneyness and PS is the strike price.
Out-of-The-Money (OTM) options were selected at 70%, 80%, 90%, and 95% of the
strike price, while In-The-Money (ITM) options were selected at 110%, 120%, and
130% of the strike price. At-The-Money options with the current price of the underlying at the strike price of the option were also included in the analytical framework.
A time series is available for all possible data cuts in terms of liquidity regime, sector,
capitalization, maturity, and moneyness.
ETFs were also examined separately as they account for a significant portion of the
trading volume in options. The same rules were applied to ETFs as to single stock
options.
34
5.5.2
Banks
A deep-dive approach was applied for the bank sector, as it is closely related to Eurozone problems and is one of the sectors most affected by financial market woes. First,
bid-ask spreads of call options on high and low capitalization banks in the United States
were compared to each other. Next, to examine differences between two different geographies, US banks were compared to European banks.
A time series was constructed from every maturity and sector, as well as subgroup in
banks, including the average volume traded and the average open interest. Results were
compared and contrasted with the behavior of liquidity indices to see whether bid-ask
spreads provide us with a picture that is consistent with other measures or proxies of
liquidity and market conditions.
5.5.3
Pinning
If the price of the underlying is close to the option’s strike price, the uncertainty around
whether the option will be exercised is large, therefore making it difficult and expensive
for the seller to accurately hedge the option. This phenomenon is called pin-risk or
pinning. In order to see how bid-ask spreads behave, individual options were followed
from 6 weeks before their expiration day until expiry. Single OTM, ATM and ITM
options were followed in order to be able to point out how the pinning phenomenon
develops in terms of moneyness, trading volume and open interest. The three options
with different moneyness were compared and contrasted for a meaningful analysis.
5.5.4
Regression model
A regression model is proposed at the end of the paper in order to create a framework,
which might be of help for future decision making, hedging, and generally risk management. An OLS multiple regression of bid-ask spreads was performed with open
interest, the VIX index, and the average days to maturity as explanatory variables. For
the regression analysis, a sample portfolio of 15 highly liquid options was used.
35
6
Results
6.1
Cross-sectoral analysis
6.1.1
Differences across tenors
Both Pinder (2003) and empirical analysis of bid-ask spread time series with different maturities confirmed that options with 1-month tenor show higher sensitivity to
changes in liquidity than other maturities. Therefore in the following sub-sections only
this tenor will be examined. Below, Table 1 shows average relative bid-ask spreads
across sectors and maturities at 90% of the strike price. The columns and rows called
”Difference” show differences between the groups within a sector and between the
liquidity regimes within those groups, respectively. Figures showing correlation of
spreads or average relative bid-ask spreads without denoting moneyness, all correspond
to the OTM space at 90% of the strike price.
Table 1: Average relative bid-ask spreads of OTM options (at 90% of the strike price)
across maturities and sectors
6.1.2
Cross-sectoral differences
In order to understand how option market liquidity of different sectors changes over
time and to compare them with each other, we examined eight sectors from the common sector classification for stocks (cash equities), both cyclical and non-cyclical ones
(sectors are shown in Table 1 and in Appendix A). Without the aim to cover the whole
spectrum of sectors and sub-sectors, the ones considered in this analysis are represen-
36
tative of similar sectors and of general interest of traders and investors. In each sector,
three high-capitalization and three low-capitalization names were taken as the group
for which option bid-ask spreads were followed and averages calculated of those. The
companies were selected from the top 10 and bottom 10 percentiles of the Yahoo.com
(2012) database in terms of market capitalization. All the sectors were examined and
two liquidity regimes were selected:
• a low liquidity period: 1 August 2011- 26 September 2011
• a high liquidity period: 1 February 2012 - March 29 2012
If not stated otherwise, the OTM options have a 90% moneyness (as defined above).
In Tables 2 to 3 and on Figures 9 to 12, one can see the daily bid-ask spreads of all
the sectors for low-capitalization and high-capitalization names in a low and a high
liquidity regime, respectively. Figures of the same capitalization groups use the same
scaling on the vertical axis for the sake of comparison. One remarkable characteristic is
the volatility of the spreads; day-to-day changes are large and tend to increase with the
average level of the bid-ask spreads specific to the various sectors. Both average levels and the amplitude of day-to-day swings tend to be lower in times of high-liquidity,
as well as for the high-capitalization groups. The average annualized volatility of the
spreads is in the 200-500% range, which means very high volatility. One reason for
this might be the possibly inappropriate choice of some of the included options. The
average annualized volatility of the spreads are shown in Table 18 in Appendix A. The
downgrade of the US long term credit rating and the escalating Greek debt crisis are
clearly recognizable in the beginning of August 2011; as macroeconomic shocks, they
trigger a jump in almost all sectors.
In the high-capitalization group, services, banks, and pharmaceuticals consistently exhibited lower average bid-ask spreads than other groups. Options on pharmaceuticals
and oil & gas companies performed similarly in the low-capitalization group, as did
banks and industrials during high and low liquidity periods, respectively.
37
Table 2: 25th, 50th and 75th percentiles of daily sector spreads distribution in the high
liquidity regime at 90% moneyness
Table 3: 25th, 50th and 75th percentiles of daily sector spreads distribution in the low
liquidity regime at 90% moneyness
38
Figure 9: Low-cap cross-sectoral bid-ask spreads in a low-liquidity regime
Figure 10: Low-cap cross-sectoral bid-ask spreads in a high-liquidity regime
39
Figure 11: High-cap cross-sectoral bid-ask spreads in a low-liquidity regime
Figure 12: High-cap cross-sectoral bid-ask spreads in a high-liquidity regime
40
• Cyclicality
Cyclical sectors (i.e. industrials) tend to have a higher spread but surprisingly
the difference between high and low liquidity regimes are rather small compared
to other sectors. Meanwhile, banks and the oil and gas sectors, the ones most exposed to financial markets, exhibit more substantial differences between the two
regimes. Interestingly, the technology sector belongs to the later group with an
8% difference in spreads. Services, internet, consumer staples, and pharmaceuticals are seemingly less dependent on liquidity. Details are shown in Table 22
in Appendix B.
• Capitalization
In all sectors, except for Oil & Gas, the low capitalization group trades with
higher average spreads. This holds true across all maturities. The difference decreases with increasing moneyness; however, this phenomenon becomes more
pronounced when the options reach the ATM territory. The reason for the unusual behavior of the Oil & Gas sector might be the relatively high-cost research
and exploration activity serving as a bias for the high capitalization group. This
can possibly trigger unexpected swings in the spot prices. We note that BP is
listed in the US but is not part of the analysis (to avoid the potential bias introduced by the Deepwater Horizon accident). Relatively high mergers and acquisition activity might also introduce a similar bias. Pharmaceuticals have smaller
than usual difference in spreads and for the ITM territory, lower spreads for
the low-capitalization group is not unimaginable for the same reasons. As mentioned in the previous paragraph, Table 22 in Appendix B contains all the details.
• Spreads across moneyness
In both liquidity regimes and almost all sectors, regardless of capitalization,
spreads widen rapidly with decreasing moneyness. In some sectors, spreads
reach as high as 30-50% for the low capitalization group at 70% and 80% moneyness. At 90% and 95% of the strike price, spreads start to tighten and reach
the ATM averages. These usually hover between 5-10% and decrease further
below 5% when the spot price climbs above 110% of the strike price, suggesting
higher certainty that the option will be exercised. Figures 13 and 14 show ex41
amples from the bank and technology sectors. Complete tables are available in
Appendix B.
Figure 13: Average bid-ask spreads across various moneyness levels in the Bank and
Technology sectors in the high liquidity regime
Figure 14: Average bid-ask spreads across various moneyness levels in the Bank and
Technology sectors in the low liquidity regime
42
• Correlation of spreads with liquidity indices
To provide the reader with a summary, we look at correlation of spreads in the examined sectors with the previously introduced fear and liquidity indices across
various maturities and moneyness levels. In terms on moneyness, correlation
with the most popular index, the VIX, appears to be the highest at 90% of the
strike price and the ATM, except for a few outliers. In the deep ITM space, correlation drops to practically 0 in most sectors as expected, due to the disappearance
of the model risk (the largest factor in the OTM space). Details can be found in
Table 19 in Appendix B. There is are clear differences between the groups in
the low liquidity regime across the board: defensive sectors such as pharmaceuticals or consumer staples exhibit positive correlation with the VIX in times of
high liquidity while sectors dependent on economic cycles and more exposed
to financial markets have a negative correlation with the same index during the
same period. Positive correlation of spreads in the banking sector with the VIX
index during a liquidity squeeze is related to the coupling between banking revenues and financial market performance. This type of coupled uncertainty acts
as an upward catalyst for the model risk. Industrials, one of the most cyclical
sectors, also have a higher correlation with the VIX index in the low liquidity
regime. The high liquidity regime means normal market conditions for most of
the sectors, therefore intuitively no high correlation is expected. This intuition
is certainly reinforced by our results. The cyclical sectors show the highest correlation (positive in the low and negative in the high liquidity period) with the
VIX index, especially during the aforementioned liquidity squeeze. Results also
suggest negative correlation of average sector spreads with 2-year Italian bond
yields. Although in absolute terms, the correlation is not high but this relationship holds true in most sectors. There are also differences between correlation
of different maturities in the same sector. Considering options with 90% moneyness: one-month maturities tend to have the highest correlation in most sectors,
followed by three-month and finally six-month options. As options get closer to
their maturity and are below the strike price, the model risk also drives correlation with the VIX, an aggregate index of volatility.
43
• Trading volume
As expected, trading volumes (only call options considered) are significantly
higher for the high capitalization group across all sectors and regardless of liquidity regimes. An interesting observation is the higher average trading volume
in the low liquidity period. This holds true for almost all sectors, industrials
being the most significant exception. Important to note, that the higher average
trading volume is often driven by extreme peaks or bursts in trading activity, followed by a longer decay. One possible explanation for the higher volume in the
low liquidity regime is that investors tend to react with a fire-sale to increasing
stress in the markets, thereby boosting trading volumes for a few days or weeks.
On the other hand, HFTs tend to react the exact opposite way: they stop trading or significantly reduce trading volumes when a vastly unexpected event or
chain of events occur. This phenomenon is discussed in Barker and Pomeranets
(2011). It is not exactly clear what the net effect of these different mechanisms is
but the fire-sale notion appears to influence the spreads to a higher extent. In the
low liquidity regime, volumes behave in a more erratic manner. For reference,
Table 22 in Appendix B also shows trading volume and open interest.
• Open interest
Open interest shows (only call options considered) a more varied picture with
the averages in the high and low liquidity regime much closer than for the trading volumes. Interestingly banks have the highest average open interest from all
sectors examined in this paper. Banks are possibly the most exposed to liquidity
squeezes in financial markets due to the way these institutions fund themselves.
Lower liquidity generally brings higher credit spreads, stricter collateral requirements, frequent margin calls and general mistrust in banks. The best example
is the fall of Lehman Brothers in 2008 ultimately triggered by serious liquidity
issues. These fears usually cause large and sudden swings in bank stock prices.
The open interest might as well be the result of this phenomenon.
In order to present the differences between high and low liquidity regimes as well as
different capitalizations in a more comprehensible way, we provide the reader with time
series charts from the technology sector. Figure 15 showcases how spreads for the low44
capitalization group stay consistently higher than those of the high-capitalization group
in the technology sector, while Figure 16 exhibits the differences between a low and a
high liquidity regime. Variation of spreads across liquidity regimes and capitalization
in the technology sector is described by Figures 17 to 20. On Figures 16 and 18 to 19,
the x-axes show a day count in order to compare the relative levels and the dynamics
of the spreads, trading volume and open interest, respectively. Higher trading volumes
and open interest in times of high liquidity and for high-capitalization companies are
rather common across all sectors, as described in Table 22 in Appendix B.
Figure 15: OTM high-cap vs. low-cap bid-ask spreads in the tech sector in a low
liquidity regime
45
Figure 16: OTM high-cap bid-ask spreads in the tech sector in a low vs. high liquidity
regime (x-axis shows a day count for the sake of comparison)
Figure 17: Tech sector high-cap vs. low cap average trading volume in a low liquidity
regime
46
Figure 18: Tech sector high-cap average trading volume in a high liquidity vs. low
liquidity regime (x-axis shows a day count for the sake of comparison)
Figure 19: Tech sector high-cap average open interest in a high liquidity vs. low
liquidity regime (x-axis shows a day count for the sake of comparison)
47
Figure 20: Tech sector high-cap vs. low-cap average open interest in a high liquidity
regime
6.2
ETFs
Exchange traded funds (ETFs) are investment funds traded publicly on exchanges. Assets in the fund can be stocks, bonds, commodities, or other assets depending on the
strategy of the fund. Many of the ETFs are index trackers: they track an index by
including the components of the index with the same % shares. However, there are
increasingly more actively managed funds which can be traded on exchanges. ETFs
provide investors with a simple and low cost solution to track and trade well-known
indices, such as the S&P 500.
ETFs are the most popular exchange traded products, trading volumes are generally
higher than those of stocks, making them a very important asset class in the investment
world. They are effective means of obtaining exposure to a certain sector, asset class,
or geography without having to worry about rebalancing the portfolio. Additionally,
ETFs have cost and tax advantages over actively managed portfolios.
For our analysis, we have selected some of the most popular ETFs (highest trading volumes) with various underlying based on ETFdb.com (2012) data. The same types of
analyses were performed with ETFs as with sector level equity options in the previous
subsection.
48
We start with a brief comparison of results with the previously described sector spreads.
In the OTM space, spreads of ETF options tend to stay below those of the previously
discussed sector spreads. Volatility of ETFs is generally lower than that of single stocks
due to their substantially lower idiosyncratic risk. This certainly drives spreads lower
as well. An opposite effect comes from the trend that most HFTs trade with ETFs,
making liquidity and the bid-ask spreads largely unpredictable. On the other hand,
another possible reason for the lower spreads is the ETF hedging activity of traders.
ETFs can be hedged through indices as a proxy, which consequently are highly liquid.
Options on the SPY (tracking the S&P 500), the ETF with the highest trading volume,
have generally the lowest spreads across all examined options. This does not come
as a surprise given the fact that the SPY is very liquid and there are no large sudden
price swings in the underlying. Options on precious metal ETFs, such as SLV (silver)
and GLD (gold), also trade with relatively low spreads. However, precious metal ETF
options have exhibited wider spreads in the high liquidity period. This unusual observation might be the consequence of the safe haven status of precious metals which are
more popular during times of liquidity squeezes, economic downturns, and bear market
periods.
The examined aggregate commodities ETF options appear to be characterized by higher
spreads compared to those mentioned above. This holds true both for UNG (United
States National Gas) and DBC (Diversified Commodities), the most-actively traded
commodity ETFs. Options on the XLF (Financial Select Sector SPDR Profile) have
somewhat wider average spreads than those on high capitalization banks or the S&P
500. On the other hand, trading volumes and open interest are high, almost reaching
those of the options on the SPY. This is consistent with the ETFdb.com (2012) data on
the underlying ETFs.
As a means to compare and contrast the financial sector with non-financials, we also
examined options on the QQQ (Nasdaq 100 Index) ETF. The QQQ includes 100 of the
largest capitalization domestic and international non-financial companies listed on the
Nasdaq exchange. Spreads of options on the QQQ proved consistently smaller than
those on the XLF. Difference in spreads between the low liquidity and high liquidity
regimes are larger than for the XLF. This is unexpected as banks are thought to be
49
more vulnerable during liquidity squeezes which is also often reflected in downward
trending and volatile stock prices. The key to the above mentioned discrepancy is to
be found in the components of the XLF index. These include regional and retail banks,
with deposit taking and lending as the main activities, which are perceived as much
more stable and less risky than investment banks and bulge brackets. Figure 21 below
supports our analysis.
Figure 21: Average bid-ask spreads of options on the most popular ETFs with 1-m
maturity in the low liquidity period
Descriptions and details of the ETFs can be found in Appendix A. In summary, ETFs
yield surprising and sometimes counterintuitive results, which might be worth a closer
and more comprehensive look.
6.3
Deep dive: bank sector
Based on the previously discussed results, general interests in banks, and for the sake
of a better picture of the special characteristics of a particular sector, we take a deep
dive into the bank sector. First, a wider set of high and low capitalization US banks are
examined, followed by a comparison of US and European banks.
50
6.3.1
High-capitalization vs. low-capitalization banks
In this section, we look at high-capitalization and low-capitalization banks from the US.
The rational for this is the vastly different business model of these banks. High capitalization banks are generally the large universal banks, involved in investment banking,
wealth management, asset management, and retail banking in some cases (Citigroup,
Bank of America, JPMorgan Chase, etc.). Low capitalization banks are typically retail
banks, some of the regional players, with a classic deposit-taking and lending activity,
along wealth management in some cases. This latter is typically considered a low-risk
business model, despite the demise of many of these banks in the sub-prime crisis due
to very high default rates on residential mortgages and credit card debt. Volatility of
the stocks in the two groups are also rather different. Stocks of the high-capitalization
group were very volatile for several reasons, including balance sheet concerns, regulatory pressure, and similarly volatile capital markets activity. Stocks of the low capitalization group were much less volatile and the market capitalization of these companies
also stayed around or above their book values. Below we discuss the most important
findings of this comparison.
• Correlation of spreads for different capitalizations
It is hard to find a pattern or trend in terms of capitalization. Neither the high
capitalization nor the low-capitalization group has a higher correlation across
maturities, fear indices, or moneyness. This certainly is not the case with the
actual averages, as we show later.
• Correlation of spreads across moneyness
We have looked at correlation with the VIX index across various moneyness levels. As shown in Table 4, correlation with the VIX is generally positive in the
low liquidity period and negative in the high liquidity period. Bank stocks have
been very volatile in the last 5 years due to general mistrust in their management
teams, their quarterly reports and their role in the subprime crisis. In addition,
concerns were lingering around their very high exposure to the global economy
and markets, which were experiencing a severe downturn over this period. Large
universal banks still mostly trade below their book value due to the fact that
investors struggle to understand and believe what is behind the assets and lia-
51
bilities disclosed on their balance sheet. Before and during the subprime crisis,
the mortgage backed securities were disclosed at much higher values than their
fair values. Banks were reluctant to write down losses from the value of these
assets, despite the high and increasing rate of non-performing loans packaged in
these securities. Regional banks have higher net asset value to book ratios but
do not reach averages of other sectors. In times of high liquidity or when there
is a general market euphoria, banks rally with little dependence on other risks.
This contributes to the negative correlation seen in this period. Our examined
high liquidity period falls after the first and partly after second LTRO which has
been a rather specific relief for the financial sector. This effect most certainly
amplifies the negative correlation to a large extent.
• Correlation of spreads across maturity
Spreads in the high capitalization group show a decreasing correlation with increasing maturity, as seen in Table 5. This holds true both for the high and the
low liquidity regime. The decrease is expected as both trading volumes and open
interest show substantial decline as tenors are stretched. Correlation in the low
capitalization group interestingly changes sign for 6 month tenors. Significance
of the results for 6 month option is very low, therefore we dismiss these findings.
• Correlation with various fear indices and liquidity proxies
From all the fear indices we considered in Table 6, the VIX has the highest
correlation with the spreads (at 90% moneyness). Correlation behaves similarly
as seen in the cross-sector analysis discussed earlier in Section 6.1.2. However,
differences between the high- and low-capitalization groups are not consistent.
On the same page, it is important to point out that the statistical significance of
correlation these values are rather low (p-values generally above 0.2) for most
indices but the VIX, the Capital Market Liquidity index and the 10-year German
government bond yields. A summary table can be found in Appendix B.
• Average spreads
As moneyness increases from 70% up to 110%, bid-ask spreads gradually decrease both in the high-capitalization and the low-capitalization group. This is
shown in Table 7. These results are consistent with our view and the results obtained earlier; liquidity of the options with different moneyness is well reflected.
52
Due to the slightly different composition of the banks in these groups (higher
number of firms), the results also show slight differences but the overall picture remains the same. Differences between the high- and the low-capitalization
group also shrink with higher moneyness.
• Trading volume
An interesting point is the trading volume: for both groups, trading volumes are
higher in the low liquidity regime. The high trading volumes are related to downtrending stock prices; we know from anecdotal evidence that this is related to a
fire sale in the low liquidity period due to the escalating European debt crisis and
concerns about collateral treatment of downgraded US treasuries. Average bidask spreads are shown in Table 7 and time series plots can be seen on Figures 22
and 23.
Table 4: Correlation of high-cap vs. low-cap banks with the VIX index across various
moneyness levels and with 1-month maturity
Table 5: Correlation of high-cap vs. low-cap banks with the VIX index across different
maturities at 90% moneyness
53
Table 6: Correlation of high-cap vs. low-cap banks with the various fear and liquidity
indices at 90% moneyness and with 1-month maturity
Table 7: Average bid-ask spreads of high-cap vs. low-cap US banks with 1-month
maturity
54
Figure 22: Average bid-ask spreads of high-cap US banks in a high-liquidity period
Figure 23: Average bid-ask spreads of high-cap US banks in a low-liquidity period
After the analysis, we conclude that spreads of both high- and low-capitalization banks
show a low correlation with the fear indices, except for the VIX index. Correlation is
generally positive in the low liquidity and negative in the high liquidity regime. Correlation (and its significance) decreases with the maturity and no clear trend can be read
across various moneyness levels. Average spreads reinforce our view that increasing
moneyness results in lower spreads.
55
6.3.2
US vs. European banks
The vast differences between US and European banks make a comparison especially interesting. In recent years, business models of these groups have started deviating from
each other. This has been driven mostly by the regulatory environment and economic
conditions of the two geographies. While US banks fall under a more lenient regulatory treatment with lower required capital ratios and reporting according to Basel I, the
European banks have seen higher required core tier 1 ratios, strict monitoring of mortgage risk weights, direct regulatory orders, and Basel 2 (Basel 2.5 and eventually Basel
3) reporting. This difference and the potential Basel 3 implementation in the US is discussed by Getter (2012). Capital requirements and restrictions on risk weighted assets
constrained European banks in pursuing similar business models (large-scale trading
operations globally, characterized by high risk weighted assets) as the US peers. Valuation of the US and European banks have also followed slightly different paths, so
did volatility of the stocks, resulting in higher model risk for European names. These
differences should also be reflected in the option bid-ask spreads.
• Spreads across moneyness
Correlation with the VIX is generally higher for ATM and ITM options in the
high liquidity period for options on European banks and lower in the low liquidity regime. As a reminder, generally the opposite is true for options for US
banks. In line with the discussion above, the correlation in the high liquidity
period is generally negative, while in the low liquidity period it is positive but
lower in absolute terms. This observation can be followed in Table 8.
• Spreads across maturities
Another interesting point is the correlation of 6-month options on European
names with the VIX index. This is higher than the correlation of 1-month and
3-month options with the same index. It is worth examining this observation in
the future in a detailed manner. Important to mention that this is not coupled
with higher average spreads for 6-month options. This is shown in Table 9.
• Fear indices and liquidity proxies
Correlation with the VIX is also pronounced here in both groups. However, an
interesting point is that the correlation of spreads of options on European names
56
with 2-year Italian Treasury spreads is negative. This goes against the common
logic which would expect positive correlation as the European sovereign debt
crisis affects trading volumes negatively and contributes to decline in liquidity.
Table 10 contains the relevant numbers.
• Average spreads
As seen before in this thesis, there is a striking drop in average spreads when
spreads get to the ATM, then into the ITM space (see Table 11 as well as Figures 24 and 25). Spreads of options on European banks tend to stay consistently
above those on US banks. The first reason for this comes from the nature of options on European names. Stocks of these European banks are listed on the New
York Stock Exchange but this is not their primary market, hence liquidity is substantially lower than on their primary market and also compared to US names.
However, the second reason is that European banks’ stocks have also exhibited
high volatility in the last few years, which in turn increases model risk of options
on them. This leads to higher spreads as market makers aim to be compensated
for the risk they take.
• Trading volume
As discussed in the previous section, the average trading volume of US banks are
higher in the low liquidity regime. The opposite is true for European banks; the
high liquidity regime has significantly higher volume. It is important to note that
the absolute average volume of the European names are much lower than that of
the US banks. This is due to the secondary listings mentioned above. However,
the relationship of the low and high liquidity regimes is consistent with the result
obtained in the cross-sector analysis.
57
Table 8: Correlation of US vs. European banks with the VIX index across various
moneyness levels with 1-month maturity
Table 9: Correlation of US vs. European banks with the VIX index across different
maturities at 90% moneyness
Table 10: Correlation of US vs. European banks with various fear indices at 90%
moneyness and with 1-month maturity
58
Table 11: Average bid-ask spreads of US vs. European banks with 1-m maturity
Figure 24: Average bid-ask spreads of US banks in a high-liquidity period
59
Figure 25: Average bid-ask spreads of European banks in a high-liquidity period
Our results reconfirmed our initial intuition that indeed spreads have different characteristics for US and European banks. Average spreads of European banks are substantially higher than those of the US banks, broadly in line with expectations. Correlation
in the high and low liquidity periods show different signs for European and US banks
in the ATM and ITM space. Also spreads of European banks show an unusual tendency in terms of correlation for increasing tenors. Most of the differences stem from
the secondary listing of these option but the deviating business models (as discussed in
Section 6.3.2) and economic as well as regulatory conditions also play a notable role
in the observed behavior.
6.4
Pin risk
As described in Section 5, the uncertainty around options with the underlying close to
the strike price, and whether they will be exercised or not, is called pin risk. To illustrate how bid-ask spreads behave when pin risk is present, we plot the bid-ask spread
time series of an OTM (strike: 645), an ATM (strike: 585) and an ITM (540) option on
the same name, Apple Inc. (the options all have the same maturity, 31 July 2012). The
options can be found in Appendix A. The moneyness regime (OTM, ITM or ATM)
here was determined on the maturity date. Not only bid-ask spreads but also trading
volumes and open interest are shown on Figures 26 to 28. Figure 29 compares the three
time series to each other. As expected, the ATM bid-ask spread produces a large jump
60
in the last few days of the examined period when the price of the underlying reaches
the strike price. The bid-ask spread of the OTM option is volatile and higher in absolute terms than the others. Also, there is no significant uptick in the last few days. The
same is true for the ITM option which stays flat over the examined time period and is
lower in absolute terms than the other two.
Trading volumes also exhibit a remarkable jump in case of the ATM options and the
open interest also shows a small increase. The opposite is true for ITM options: both
trading volumes and open interest show a substantial drop towards the maturity date.
Trading volumes of the OTM option show a substantial jump close to the maturity date.
This might be the result of a similar sudden increase in moneyness.
Figure 26: Apple OTM option
61
Figure 27: Apple ATM option
Figure 28: Apple ITM option
62
Figure 29: Apple OTM vs. ATM vs. ITM in July
6.5
Regression model of bid-ask spreads
In order to provide the reader with an example of practical application of liquidity
research on option market bid-ask spreads, we aim to introduce an illustrative regression model. Currently, literature does not indicate that financial institutions use similar
models for quantifying liquidity risk. Informal discussions with risk managers and
practitioners also led to the conclusion that no wide-spread systematic methods are
used today to quantify liquidity risk. The benefit of such a model lies in its circle of application, including risk control and management, hedging and decision-making. For
example, if a liquidity risk model indicated that the liquidity of securities in a portfolio
fell to a dangerously low level, alarms would indicate this to traders (who could try to
sell down part of the assets or hedge them appropriately), risk managers (who could
develop strategies to hedge the portfolio or indicate this to the risk oversight committee) and product controllers (who could adjust the current value in the books, based
on liquidity risk). These models and methods are certainly have to be tailored to the
different needs and characteristics of particular trading desks. Regulators are currently
not requiring financial institutions to account for or systematically measure liquidity
risk but this might change soon.
The regression model can be built on various exogenous and endogenous measures
used as explanatory variables. In general, exogenous variables might include commonly used indices (e.g., the VIX index) or proxies for market-wide liquidity (e.g.,
63
Italian sovereign bond yields). Endogenous variables here mean measures related to
the examined options (e.g., moneyness, trading volume, open interest, etc.). Here, we
aim to use the observations made in the previous sections to set up realistic and sensible
models.
The modeling work and testing were performed using SPSS from IBM Corp. (2012).
We performed the regression analysis considering both the low liquidity and high liquidity period introduced in Section 6.1.2. The models were built on a sample portfolio
of 15 highly liquid options with 3-month maturities (exceptions were made where the
3-month option was not an appropriate choice for availability or liquidity reasons) and
the moneyness close to 90% at the end of the examined periods (we allowed a 4% tolerance interval due to availability reasons). The options used in both liquidity regimes
can be found in Appendix A.
First, a linear multivariate regression model was built using OLS (ordinary least squares)
regression. The dependent variable was the relative bid-ask spread. Initially we considered the following explanatory variables: trading volume (daily), moneyness, time
to maturity, open interest and the VIX index. We chose the VIX index because the
bid-ask spreads showed the highest correlation with this index in the previous sections.
A dummy variable was also introduced for the liquidity regime (with a value of 1 for
the low liquidity regime and a value of 0 for the high liquidity regime), as the two
periods were examined together (controlling for the liquidity regime). SPSS was used
to find the model with the best fit, measured by its R2 . For the analysis, an α of 0.05
was used, meaning a 95% confidence interval (this translates to an upper boundary for
significance of 0.05 for the explanatory variables’ p-value). To find the best model, the
following procedures were used: all variables included, forward selection, backward
elimination, and stepwise regression. The latter three procedures all yielded the same
model shown below. When all variables were included, the R2 was 0.03 higher but
the significance of certain explanatory variables was very low (p-value substantially
higher than 0.05). During the iteration process to the simple linear model, moneyness,
the dummy variable for the liquidity regime and the trading volume were excluded due
to their low significance (p-value substantially higher than 0.05).
The obtained simple multiple regression model is the following:
64
BAS = β0 + β1 int + β2 V IX + β3 time + ,
where BAS is the bid-ask spread, β0 is the constant term (or intercept), β1 to β3 are
the coefficients, int is the open interest, V IX is the VIX index, time is the days to
maturity and is the independent identically distributed normal error.
The R2 of the model, denoting the goodness of fit, is 0.646. This can be considered
as a relatively good fit but not an exceptionally high one. The model summary can be
seen in Table 25 in Appendix C; under Model 3. The coefficients and their statistical
significance, measured by their p-value, are shown below in Table 12. β0 to β3 are
listed in the ”B” column under ”Unstandardized Coefficients”, in the respective order.
All the included explanatory variables show high statistical significance. So does the
overall significance of the model based on an F-test (the p-value is smaller than 0.001),
as shown in Table 13. In essence, the high significance means that there is indeed a
linear relationship between the variables in our model.
Table 12: The coefficients of the simple linear model
Table 13: The ANOVA table of the simple linear model
The graphical comparison of the actual and the fitted values is shown on Figure 30
and 31.
65
Figure 30: The comparison of the actual and the predicted values for the simple linear
model in the low liquidity period
Figure 31: The comparison of the actual and the predicted values for the simple linear
model in the high liquidity period
Based on the graphical comparison, we can argue that the fit is not particularly good
in the high liquidity period. In order to be able to draw inferences from the model,
we have to check the assumptions, on which our linear multiple regression model was
built. Without this, the t-tests of the coefficients are not meaningful.
The assumptions are the following: the response variables have to be normally distributed, independent, and their variance has to be constant. In addition we also have to
examine whether there is multicollinearity present (high correlation or covariance between the explanatory variables) in the model. To test whether the model violates these
66
assumptions, we have to examine the standardized residuals of the model. The normality is examined using the standard Kolmogorov-Smirnov and Shapiro-Wilk tests. The
results are shown in Table 14.
Table 14: The normality test of the simple linear model
The p-value of the Kolmogorov-Smirnov test is 0.051, which suggests that normality
assumption might be violated. The Shapiro-Wilk test yielded a statistical significance
smaller than 0.001, measured by the p-value, indicating that normality is indeed a problem here.
The multicollinearity is already tested and the variance influence factors (VIF) are
shown in Table 12. The VIFs of all the coefficients are substantially lower than 5, the
commonly considered threshold for multicollinearity issues, as suggested by O’brien
(2007). This means that we do not have a multicollinearity problem with this model.
The autocorrelation of the residuals was also already tested with the Durbin-Watson
test and the result is shown in Table 25. The Durbin-Watson statistics here is 1.137,
indicating that the autocorrelation is not prevalent. According to Wang and Jain (2003),
for small sample sizes, the rule of thumb is that if the Durbin-Watson statistics is between 1 and 2.5, the lack of autocorrelation should be accepted.
The constant variance, or homoscedasticity, is tested with the Breusch-Pagan test. Our
H0 hypothesis for the test is homoscedasticity. The test resulted in a significance of
0.000, which means we reject the H0 hypothesis and conclude that the residuals are
heteroscedastic. The output of the test is shown on Figure 34 in Appendix C.
The results suggest that the OLS estimates can not be strictly considered the best unbiased linear estimates (BLUE) due to heteroscedasticity. The linear relationship and the
unbiased nature of the variables have been shown before and the zero mean condition
67
of the BLUE was also met (0 mean for the residuals). The latter is shown in Table 26
in Appendix C. However, the homoscedasticity and the normality conditions were not
fulfilled. Normality is not a condition of BLUE but required for meaningful t-test results. In order to find a model which fulfills all the requirements, and therefore can be
used to make inferences from it, we have to modify our model introduced above by
transforming some of the variables.
Using the curve fitting function of SPSS and running a Box-Cox analysis led to the
appropriate transformation of our variables. Important to note that after the transformations, the model is still linear and the OLS method can be applied. On the bid-ask
spreads, we applied a Box-Cox transformation (to normalize the data) with a λ = −3
due to the non-normality of the residuals. The Box-Cox transformation is described
by Sakia (1992) the following way:
(
(λ)
yi
=
yiλ −1
λ ,
log(yi ),
if λ 6= 0,
if λ = 0,
where y is the transformed variable and λ is the parameter. The explanatory variables were also transformed: int3 , V IX 2 and time2 proved to yield the best results.
The new model was tested the same way as the simple linear model described above.
All conditions were met, except homoscedasticity. In general, there are two ways to
correct the model for homoscedasticity. First, the OLS regression can be used with
heteroscedasticity-robust standard errors, which does not require assumptions on the
nature of heteroscedasticity. Second, a weighted least squares (WLS) regression can
be used if we know the nature of heteroscedasticity. Here, we do not have information on the nature of heteroscedasticity, thus we use the first solution. To estimate
heteroscedasticity-robust standard errors and to test the new model, we used the SPSS
macros written by Hayes (2007).
The model summary is shown in Table 15. The Durbin-Watson statistics indicates that
there is no autocorrelation.
Table 15: The model summary of the final model
68
The coefficients and the standard errors are shown below in Table 16. The p-values
show that all coefficients are statistically significant. The variance influence factors
are substantially lower than the threshold, as discussed earlier, which means multicollinearity is not a problem in this model.
Table 16: The coefficients of the final model
The normality condition is now met, as shown in Table 17 below.
Table 17: The normality test of the final model
The problem with heteroscedasticity is avoided by using heteroscedasticity-robust standard errors. The transformed spreads and the predicted values are shown on Figures 32
and 33. The predicted values certainly fit the data to a higher extent than before. This
can also be seen from the R2 of 0.834 and the Adjusted R2 of 0.827 as shown in Table 15. This means that 83% of the variance in the data can be accounted for by the
explanatory variables; this can be considered sufficiently high. The final OLS model
now fulfills all conditions and thus can be used to make inferences based on the t-tests
of the variables.
The obtained final multiple regression model is the following:
T BAS = β0 + β1 int3 + β2 V IX 2 + β3 time2 + r ,
where T BAS is the Box-Cox transformed relative bid-ask spread. The estimators are
still not regarded as best but they remain unbiased and linear, in addition to the fulfilled
normality condition and heteroscedasticity robustness. For the purpose of our current
analysis, this is already sufficient.
69
Figure 32: The comparison of the transformed spread and the predicted values for the
final model in the low liquidity period
Figure 33: The comparison of the transformed spread and the predicted values for the
final model in the high liquidity period
7
Conclusions
In this thesis, several aspects of option market liquidity were examined with a special
focus on bid-ask spreads of call options (as call and put options are regarded as sub-
70
stitutes). We started with the review of existing literature both on the broadly and narrowly defined topic in order to give an overview of results and research trends. There
is a sufficient number of published papers on the components and main determinants
of bid-ask spreads: order processing cost, inventory holding cost, model risk, as well
as hedging and rebalancing cost. Literature on option market bid-ask spreads proved to
be thin and certainly not comprehensive. Available information on characteristics and
behavior of bid-ask spread time series were even harder to find.
After discussing the advantages and disadvantages of various liquidity measures, we
concluded that relative bid-ask spreads are adequate for the purpose of our analysis:
examining differences between bid-ask spreads across sectors, maturities, liquidity
regimes and underlying securities.
After providing a macroeconomic backdrop, we went on to perform the above mentioned set of analysis, always considering a high and a low liquidity regime along
with a high and low capitalization group across maturities. Our results show that high
liquidity and high capitalization indeed lead to tighter spreads, as expected. The picture is mixed when it comes to differences between sectors. Cyclical sectors tend to
have higher spreads then non-cyclicals but the difference in spreads between high and
low liquidity regimes are not as large as in other sectors. Interestingly, the volatility
of option bid-ask spreads are rather substantial in almost all sectors. Examining the
correlation with well-known liquidity and fear indices also yielded surprising results:
correlation changes sign for some sectors (i.e. the banking sector) between the two liquidity regimes. The absolute values of correlation also vary between liquidity regimes
with low liquidity meaning higher correlation. We also showed visual examples from
the technology sector to improve the understanding of dynamic changes and differences implied by liquidity and capitalization.
We have also looked at options on the most popular (in terms of trading volume) ETFs
and concluded that they generally exhibit significantly lower spreads then options on
stocks. Options on the S&P 500 and precious metals traded with the lowest spreads,
while commodities and financials ETFs had somewhat higher spreads.
After the cross-sectoral analysis, we performed a deep-dive in the bank sector as this
71
one is the most exposed to liquidity squeezes and generally to changes in liquidity (as
also shown in the correlation table). Both the high capitalization group and the group
consisting of US universal banks exhibited substantially lower spreads than the low
capitalization group and the one composed of European names, respectively.
Finally, we examined a phenomenon specific to the option market: the pin risk. Results
show that bid-ask spreads of ATM options widen rapidly and steeply when the maturity
is only a few days away. This is consistent with the increased risk and therefore the
decreased willingness of market makers to provide liquidity in these stocks. The same
behavior is, as expected, not witnessed for ITM and OTM options, which supports our
ideas of how liquidity affects bid-ask spreads.
Based on the differences in spreads and their behavior over time, we have set up two illustrative multiple regression models for a sample portfolio of options. The first model
is a simple linear model, which serves as an introduction to the more sophisticated
second one. The final OLS model uses the cubic function of open interest, along with
the square functions of the VIX index and the average days to maturity as explanatory
variables. The dependent variable is the Box-Cox transformed relative bid-ask spread.
The model fulfills all assumptions required to use the results of t-tests and therefore
suitable for further analysis or customization for practical use. Extended versions of
this model can be used for purposes of risk management and hedging as well as fair
value adjustments based on liquidity risk.
8
Outlook
As discussed in the introduction, the current thesis does not intend to serve as comprehensive guide to liquidity in option markets but aims to examine the characteristics
of bid-ask spreads and how they behave for various groups and liquidity regimes. In
addition, it tries to grasp to what extent can bid-ask spreads be considered a good proxy
measure of liquidity.
As a follow up to the current work, the next step would be an extended set of groups
across all sectors with a more granular breakdown of moneyness. Time intervals could
also be extended and pre-crisis years could be examined to see whether the tighten72
ing spreads and then the sudden dry-up of liquidity were indeed reflected in bid-ask
spreads. Given options data is available, a larger-scale analysis on the differences between options with US and European stocks as underlying is desirable.
Finally, the regression model needs to be calibrated to real-life portfolios to serve as
a practical tool. Other available explanatory variables may also be considered. Nevertheless, the models need to be readjusted after a certain period of time to reflect the
liquidity regime, the changes in components of the portfolio, as well as the changes in
the above discussed components of the bid-ask spreads. This would lead to a practical
way to account for changes in liquidity and would help to quantify the related risk in
option markets.
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A
Appendix A
Sector quotes:
Banks high-cap: JPM, BAC, C (JPMorgan Chase, Bank of America, Citigroup)
Banks low-cap: STI, KEY, ZION (Suntrust Banks, Keycorp, Zions Bancorporation)
Energy & Oil high-cap: XOM, PTR, RDS.A (ExxonMobil, Petrochina, Royal Dutch
Shell)
Energy & Oil low-cap: MPC, HES, MUR (Marathon Petroleum, Hess, Murphy Oil)
Consumer staples high-cap: KFT, GIS, KO (Kraft Foods, General Mills, Coca Cola)
Consumer staples low-cap: DMND, CPB, DF (Diamond Foods, Campbell Soup, Dean
Foods)
Industrials high-cap: GE, SI, ETN (General Electric, Siemens, Eaton)
Industrials low-cap: ABAT, FSIN, XIDE (Advanced Battery, Fushi Copperweld, Exide
Technologies)
Healthcare high-cap: MRK, PFE, JNJ (Merck, Pfizer, Johnson & Johnson)
Healthcare low-cap: ABT, VTUS, IPXL (Abott Laboratories, Astex Pharmaceuticals,
78
Vetrus, Impax Laboratories)
Internet high-cap: AOL, GOOG, YHOO (AOL, Google, Yahoo)
Internet low-cap: HSTM, WWW, TZOO (Healthstream, Web.com Group, Travelzoo)
Utilities high-cap: SO, DUK, EXC (Southern Company, Duke Energy, Excelon)
Utilities low-cap: EDE, ORA, BKH (Empire District Electric, Ormat Technologies,
Black Hills Coporation)
Services high-cap: WMT, TGT, COST (Wal-Mart, Target, Costco)
Services low-cap: PSMT, FDO, DLTR (PriceSmart, Family Dollar Stores, Dollar Tree)
Technology high-cap: AAPL, DELL, HPQ (Apple, Dell, HP)
Technology low-cap: LXK, SSYS, OMCL (Lexmark, Stratasys, Omnicell)
ETFs 1 :
SPX: SPDR S&P Profile S&P 500 index
The S&P 500 index measures the performance of the large capitalization sector of the
U.S. equity market.
IWM: Russell 2000 Index Fund Profile
The Russell 2000 Index measures the performance of the small-cap segment of the U.S.
equity universe and is comprised of the smallest 2000 companies in the Russell 3000
Index, representing approximately 10% of the total market capitalization of that Index.
It includes approximately 2000 of the smallest securities based on a combination of
their market cap and current index membership.
SLV: Silver Trust Profile
This ETF is designed to track the spot price of silver bullion.
GLD: SPDR Gold Trust Profile
1 Descriptions
from http://www.etfdb.com
79
This ETF is designed to track the spot price of gold bullion.
UNG: United States Natural Gas Fund LP Profile
The underlying assets of the fund consist of natural gas futures contracts.
DBC: DB Commodity Index Tracking Fund Profile
The DBIQ Optimum Yield Diversified Commodity Index Excess Return is a rulesbased index composed of futures contracts on 14 of the most heavily-traded and important physical commodities in the world.
XLF: Financial Select Sector SPDR Profile
The index includes companies from the following industries: diversified financial services; insurance; commercial banks; capital markets; real estate investment trusts; thrift
& mortgage finance; consumer finance; and real estate management & development.
QQQ: QQQ Profile
The index includes 100 of the largest domestic and international non-financial companies listed on the Nasdaq Stock Market based on market capitalization.
High-cap vs. low-cap banks:
Bank high-cap: JPM, BAC, GS, MS, WFC (JPMorgan Chase, Bank of America, Goldman Sachs, Morgan Stanley, Wells Fargo)
Banks low-cap: RF, STI, CMA, ZION, PBCT (Regions Financial Corp, Suntrust Banks,
Comerica Inc., Zions Bancorp, People’s United Financial Inc.)
US vs. European banks:
US banks: JPM, BAC, GS, MS, WFC (JPMorgan Chase, Bank of America, Goldman
Sachs, Morgan Stanley, Wells Fargo)
European banks: UBS, CSGKF, DB, BNP, HBC (UBS, Credit Suisse, Deutsche Bank,
BNP Paribas, HSBC)
80
Pin-risk quotes:
OTM: AAPL 120317C00645000
ATM: AAPL 120317C00585000
ITM: AAPL 120317C00540000
Options used in the regression analysis
Low liquidity period:
JPM 111022C00033000, GS 111022C00110000, MS 111022C00016000, C 111022C00033000,
BAC 111022C00008000, AAPL 111022C00410000, JNJ 111022C00070000, GE 111022C00019000,
GOOG 111217C00555000, WMT 111217C00055000, KO 111119C00072500, XOM
111022C00080000, DELL 111119C00016000, HPQ 111119C00025000, SO 111119C00045000,
YHOO 111022C00017000
High liquidity period:
JPM 120616C00047000, GS 120421C00130000, MS 120421C00022000, C 120519C00040000,
BAC 120519C00011000, AAPL 120421C00610000, JNJ 120421C00070000, GE 120421C00022000,
GOOG 120616P00670000, WMT 120616C00065000, KO 120519C00077500, XOM
120421C00095000, DELL 120818C00018000, HPQ 120519C00025000, SO 120519C00047000,
YHOO 120519C00017000
B
Appendix B
Table 18: Average annualized volatility of OTM (at 90% of the strike price) bid-ask
spreads across sectors
81
Table 19: Cross-moneyness correlation with the VIX index
Table 20: Cross-index correlation of OTM (at 90% of the strike price) bid-ask spreads
Table 21: Cross-maturity correlation with the VIX index at 90% moneyness
82
Table 22: Average bid-ask spread, trading volume and open interest across sectors
83
Table 22: cont.
84
Table 23: Statistical significance of correlation coefficients of the bank sector (pvalues)
85
Table 24: Average bid-ask spread of options on the most popular ETFs with 1-m maturity
86
C
Appendix C
Results of the multiple regressions:
Table 25: Model summary of the simple linear model
Figure 34: The output of the Breusch-Pagan test for the simple linear model
87
Table 26: The residual statistics of the simple linear model
88