From Funding Liquidity to Market Liquidity:
Evidence from the Index Options Market
Zhiping Zhou,
Chunbo Liu,
Cheng Zhang
1 Wuhan University
2 Norwegian School of Economics
3 London School of Economics and Political Science
27 August 2016
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Motivation
Brunnermeier and Pedersen (2009)
Provide a model that elaborates on the relationship between
funding liquidity and market liquidity (FL-ML)
Show that the two notions are mutually reinforcing, leading to
liquidity spirals
Duffie (2010, 2012)
Financial crisis increases the cost of intermediation and thus lead
to increase in trading spreads (2010 AFA presidential address)
Investors and issuers of securities would find it more costly to
borrow, raise capital, invest, and obtain liquidity (2012)
However, the implications of these recent important theoretical
findings have not been fully investigated from an empirical point
of view
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Motivation
Chordia, Sarkar, and Subrahmanyam (2005)
Explore liquidity movements in stock and Treasury bond markets
(1800 trading days)
Establish a link between macro liquidity, or money flows, and
micro or transactions liquidity
Hameed, Kan and Viswanathan (2010)
Test the relationship between funding liquidity and market liquidity in the stock market
Mancini, Ranaldo, and Wrampelmeyer (2013)
Use intraday trading and order data to measure liquidity in the
foreign exchange (FX) market
Show that negative shocks in funding liquidity lead to significantly lower FX market liquidity
Target: this paper analyzes the impact of funding liquidity on
index options market liquidity
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Results Preview
Using daily data on option market liquidity, this paper relates
index options market liquidity to measures of funding liquidity
as well as liquidity of equity markets
We find a positive relationship between option market liquidity
and funding liquidity
The put option liquidity is more closely related to funding liquidity than call options
The FL-ML relationship can be found for short-term options
Out-of-the-money and at-the-money options exhibit higher sensitivity to funding liquidity than in-the-money ones
The lower the implied volatility (IV), the larger the impact of
funding liquidity on market liquidity
Consistent with the predictions of Brunnermeier and Pedersen
(2009), we find that when funding liquidity is low, option market liquidity becomes sensitive to changes in funding liquidity
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Data and variables
OptionMetrics IVYDB: daily closing bid and ask quotes, daily
volume and open interest on S&P 500 options traded on the
CBOE market
Time span: Jan 17, 2003 - Jan 30, 2012.
Sample size: 2,265 days = 223,447 obs.
Option market liquidity measures (Cao and Wei 2010)
Proportional Bid-ask spread (PBA)
PJ
askj −bidj
j=1 VOLj ∗ (askj +bidj )/2
PJ
j=1 VOLj
PJ
Trading Volume (VOL) j=1 VOLj
PJ
Dollar trading volume (DVOL) j=1 VOLj (askj + bidj ) /2
Funding liquidity measures
TED spread from Federal Reserve Bank in St.Louis
Net acquisition of financial assets by security brokers and dealers
from flow of funds account provided by Federal Reserve Statistical Release.
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Summary statistics
Panel A: Option Liquidity
Bid-ask spread
Volume
Statistics
All options
Call options
Put options
Statistics
Option bid-ask spread
Option volume
Option dollar volume
Mean
11.84
12.67
11.19
Median
11.40
11.99
10.44
Std.
4.34
5.21
4.62
Mean
2.86
2.54
3.14
Median
2.71
2.37
2.94
Dollar Volume
Std.
1.24
1.15
1.47
Mean
7.03
6.32
7.58
Median
5.46
4.99
5.60
Std.
5.87
5.02
6.94
Panel B: The Level of Key Variables in Sub-Periods
Jan. 2003 - Jul. 2007
Aug. 2007 - Jun. 2009
Jul. 2009 - Jan. 2012
Mean
12.82
2.28
3.46
Mean
11.68
3.32
8.58
Median
12.37
1.90
2.87
Std.
4.75
1.18
2.08
Mean
9.69
3.62
13.51
Median
9.18
3.46
11.45
Std.
3.52
1.05
7.58
Median
11.54
3.21
7.57
Std.
3.46
0.94
3.93
Compared with call options, puts have a smaller bid-ask spread and a larger
trading volume
High liquidity for puts might be caused by the high transaction activities
of the informed traders during the Great Recession
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Econometric Model
We utilize an ARMAX model to analyze the relationship between funding liquidity and option market liquidity
OLt = α + β1 FLt−1 + β2 VIXt−1 +
p
X
ρi OLt−i +
i=
q
X
θj t−j + t
j
OLt is the option market liquidity on day t
FL is the funding liquidity measure and VIX is the proxy for
market uncertainty
An optimal number of lags p and q is selected based on information criteria
We expect β1 to be positive and β2 to be negative
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Empirical Results
Dependent var.
Sample
L.VIX
L.TED Spread
bid-ask
All
bid-ask
All
bid-ask
Call
bid-ask
Put
-0.109***
(-8.47)
0.649***
(2.76)
-0.124***
(-4.49)
1.358*
(1.71)
-0.001
(-0.80)
(4,3)
2264
-0.099***
(-2.73)
0.644
(0.61)
-0.132***
(-4.15)
2.036**
(2.40)
(2,2)
2264
(3,3)
2264
Acq2
ARMAX
N
OLS
1302
one-σ ↑ in VIX → PBA ↓ by 1.1 bps (25% of one-σ)
one-σ ↑ in TED → PBA ↑ by 0.65 bps (18% of one-σ)
Options market liquidity declines when liquidity providers face higher funding cost (Brunnermeier and Pedersen 2009)
We can only find a positive relationship between PBA spread and TED
spread for the subsample of puts
Puts are favoured by informed traders to realize their information value
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Option liquidity: the effect of maturities
L.TED Spread
L.VIX
N
Model
Short
1.572*
(1.72)
-0.154***
(-4.63)
2263
ARMAX(4,3)
Medium
-0.149
(-0.30)
-0.062***
(-2.88)
2263
ARMAX(4,3)
Long
-0.249
(-0.82)
-0.016
(-1.24)
2257
ARMAX(4,3)
A reduction of funding liquidity is followed by lower short options liquidity
Medium-maturity option liquidity is impacted by VIX
Long-maturity option liquidity does not respond to TED or VIX
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Option liquidity: the effect of moneyness
L.TED Spread
L.VIX
ARMAX(p,q)
N
OTM
3.136**
(2.16)
-0.275***
(-4.53)
(2,3)
2264
ATM
1.682*
(1.85)
-0.123***
(-3.76)
(2,1)
2264
ITM
0.490
(1.40)
-0.002
(-0.15)
(1,2)
2262
DOTM
0.101
(0.43)
0.016
(1.53)
(1,1)
2262
DITM
0.410***
(3.30)
0.032***
(5.94)
(3,2)
1639
TED spread is positively related to the PBA spread, implying the liquidity
of options with different moneyness declines when funding costs are high
VIX is negatively correlated with market liquidity of OTM, ATM, and ITM,
implying increase in uncertainty is followed by an increase in market liquidity
The coefficients become positive for DITM and DOTM. This might due to
the fact that investors have to afford a high cost in transactions
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Option liquidity: the effect of implied volatility
Implied volatility
L.TED Spread
L.VIX
ARMAX(p,q)
N
(1)
IV1
10.008*
(1.70)
1.109***
(5.36)
(2,3)
1166
(2)
IV2
9.518***
(3.67)
0.608***
(7.23)
(2,1)
1648
(3)
IV3
9.790***
(3.63)
-0.021
(-0.13)
(2,2)
1919
(4)
IV4
3.427
(0.95)
-0.447*
(-1.84)
(3,2)
1788
(5)
IV5
-4.226
(-1.03)
-0.762***
(-4.22)
(3,2)
1279
A monotonic decline in VIX coefficients and an almost monotonic decline
in TED spread coefficients from IV1 to IV 5
Investors would like to sell options with high implied volatility levels during
the periods of high market uncertainty
The liquidity of options with high implied volatility increases
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Stock market liquidity
Liquidity measure
Weight
L.vix
L.TED Spread
BAHL ew
High-Low
equal
-0.155***
(-5.38)
1.093
(1.31)
1.982***
(9.14)
BAHL vw
High-Low
volume
-0.160***
(-5.28)
1.244
(1.44)
Close
equal
-0.117***
(-4.31)
1.527*
(1.94)
Close
volume
-0.128***
(-4.76)
1.450*
(1.77)
Volume
Dollar
-0.138***
(-4.54)
1.391*
(1.66)
-0.139***
(-4.62)
1.587*
(1.90)
2.075***
(8.94)
BAClose ew
0.504
(0.74)
BAClose vw
25.011***
(3.15)
Stock Volume
0.280***
(4.95)
Stock Dollar
ARMAX(p,q)
N
(4,3)
2263
(4,3)
2263
(4,3)
2263
(4,3)
2263
(4,3)
2263
0.010***
(5.86)
(4,3)
2263
After controlling the VIX and equity market liquidity, there is still a positive
relationship between options market liquidity and funding liquidity
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The crisis
Sample Period
L.VIX
L.TED Spread
ARMAX(p,q)
N
(1)
(2)
Dollar volume
Pre
Post
0.386*** 0.567***
(17.29)
(22.40)
0.619
-2.306***
(0.97)
(-3.08)
(2,1)
(2,2)
1140
1124
(3)
(4)
Volume
Pre
Post
0.066*** 0.055***
(4.40)
(7.35)
0.316
-0.362*
(0.72)
(-1.76)
(2,1)
(2,2)
1140
1124
The TED spread is strongly negatively related to the dollar trading volume
for the post-crisis period, but its coefficient is not significant for the precrisis period, implying a reduction of funding liquidity is followed by lower
dollar trading volume
Consistent with the theoretical predictions of Brunnermeier and Pedersen
(2009), there are higher comovement in liquidity and higher impact of
funding liquidity on market liquidity during the crisis
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Conclusions
We provide evidence of a positive relationship between funding
liquidity and option market liquidity during the periods of high
market uncertainty
Sub-sample analysis helps uncover interesting phenomenon in
the option market
The liquidity of puts and calls responds asymmetrically to downward market movements
The liquidity of short maturity options is positively related with
funding liquidity
Options with different Moneyness and implied volatility behave
differently
Sub-sample analysis of pre- and post- August 2007 means that
when funding liquidity is low during the the recessions, market
liquidity becomes sensitive to changes in funding liquidity
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Future Research
One natural extension would be the in-depth examination of
the relationship of funding liquidity and options market liquidity
using a panel data sample
Another area of future research would be to investigate the
effect of funding liquidity on the pricing of index options
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