Liquidity Effect in OTC
Options Markets:
Premium or Discount?
Prachi Deuskar
Anurag Gupta
Marti G. Subrahmanyam
Primary Objective
 How does illiquidity affect option prices?
We study this question in the Euro OTC options
markets (interest rate caps/floors)
Anurag Gupta, NYU - Case
Related Literature – Equity Markets
 Illiquid / higher liquidity risk stocks have lower prices
(higher expected returns)

Amihud and Mendelsen (1986), Pastor and Stambaugh
(2003), Acharya and Pedersen (2005), and many others
Anurag Gupta, NYU - Case
Related Literature – Fixed Income Markets
 Illiquidity affects bond prices adversely
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Amihud and Mendelsen (1991), Krishnamurthy (2002),
Longstaff (2004), and many others
More recent papers include Chacko, Mahanti, Mallik,
Nashikkar, Subrahmanyam (2008) and Mahanti, Nashikkar,
Subrahmanyam (2008)
Anurag Gupta, NYU - Case
Related Literature – Derivative Markets
 Relatively little is known
 Vijh (1990), Mayhew (2002), Bollen and Whaley
(2004) present some evidence from equity options
 Brenner, Eldor and Hauser (2001) report that nontradable currency options are discounted
 Longstaff (1995) and Constantinides (1997) present
theoretical arguments why illiquid options should be
discounted
Anurag Gupta, NYU - Case
How should illiquidity affect asset prices?
 Negatively, as per current literature
 Conventional wisdom: More illiquid assets must have
higher returns, hence lower prices
 The buyer of the asset demands compensation for
illiquidity, while the seller is no longer concerned
about liquidity
 True for assets in positive net supply (like stocks)
 Is this true for assets that are in zero net supply,
where the seller is concerned about illiquidity, and
also about hedging costs?
Anurag Gupta, NYU - Case
How should liquidity affect derivative prices?
 Derivatives are generally in zero net supply
 Risk exposures of the short side and the long side
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may be different (as in the case of options)
Both buyer and seller continue to have exposure
even after the transaction
The buyer would demand a reduction in price, while
the seller would demand an increase in price
If the payoffs are asymmetric, the seller may have
higher risk exposures (as is the case with options)
Net effect is determined in equilibrium, can go either
way
Anurag Gupta, NYU - Case
How should illiquidity affect OTC option
prices?
 Caps/floors are long dated OTC contracts
 Mostly institutional market
 Sellers are typically large banks, buyers are
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corporate clients and some smaller banks
Customers are usually on the ask-side
Buyers typically hold the options, as they may be
hedging some underlying interest rate exposures
Sellers are concerned about their risk exposures, so
they may be more concerned about the liquidity of
the options that they have sold
Marginal investors likely to be net short
Anurag Gupta, NYU - Case
Unhedgeable Risks in Options
 Long dated contracts (2-10 years), so enormous
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transactions costs if dynamically hedged using the
underlying
Deviations from Black-Scholes world (stochastic
volatility including USV, jumps, discrete rebalancing,
transactions costs)
Limits to arbitrage (Shleifer and Vishny (1997) and
Liu and Longstaff (2004))
Option dealers face model misspecification and
biased paramater estimation risk (Figlewski (1989))
Some part of option risks is unhedgeable
Anurag Gupta, NYU - Case
Upward Sloping Supply Curve
 Since some part of option risks is unhedgeable
 Option liquidity related to the slope of the supply
curve
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Illiquidity makes it difficult for sellers to reverse trades – have
to hold inventory (basis risk)
Model risk – fewer option trades to calibrate models
 Hence supply curve is steeper when there is less
liquidity
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Wider bid-ask spreads
Higher prices, since dealers are net short in the aggregate
Anurag Gupta, NYU - Case
Data
 Euro cap and floor prices from WestLB (top 5
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German bank) Global Derivatives and Fixed Income
Group (member of Totem)
Daily bid/ask prices over 29 months (Jan 99-May01)
– nearly 60,000 price quotes
Nine maturities (2-10 years) across twelve strikes
(2%-8%) – not all maturity strike combinations
available each day
Options on the 6-month Euribor with a 6-month reset
Also obtained Euro swap rates and daily term
structure data from WestLB
Anurag Gupta, NYU - Case
Sample Data (basis point prices)
Euro Caps/Floors Caps 2.00%
1 Jahr (vs 3M)
2 Jahre
3 Jahre
636-657
4 Jahre
933-964
5 Jahre
1228-1269
6 Jahre
7 Jahre
8 Jahre
9 Jahre
10 Jahre
2.50%
3.00%
281-291
211-220
521-540
409-425
777-805
627-649
1034-1072 847-877
1300-1345 1078-1116
1310-1356
Anurag Gupta, NYU - Case
4.00%
92-99
213-227
360-378
515-540
680-712
847-887
1021-1069
1187-1241
5.00%
6.00%
99-111
189-204
292-314
402-430
515-550
640-683
760-810
866-923
45-53
98-110
165-182
236-260
311-341
400-437
482-525
557-607
Data Transformation
 Strike to LMR (Log Moneyness Ratio) –logarithm of
the ratio of the par swap rate to the strike rate of the
option
 EIV (Excess Implied Volatility) – difference between
the IV (based on mid-price) and a benchmark
volatility using a panel GARCH model
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Using IV removes term structure effects
Subtracting a benchmark volatility removes aggregate
variations in volatility
Hence it’s a measure of “expensiveness” of options
Useful for examining factors other than term structure or
interest rate uncertainty that may affect option prices
Anurag Gupta, NYU - Case
Scaled bid-ask spreads (Table 2)
Anurag Gupta, NYU - Case
Panel GARCH Model for Benchmark
Volatility
 Panel version of GJR-GARCH(1,1) model with square
root level dependence
f t ,T   0  1 f t 1,T   t ,T ,
 t ,T ~ N 0, ht2,T 
ht ,T   t ,T f t 1,T
 t2,T   0  1 t21,T   2 t21,T   3 t21,T I t1,T ,
I t1,T  1 if  t-1,T  0
 Two alternative benchmarks for robustness:
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Simple historical vol (s.d. of changes in log forward rates)
Comparable ATM diagonal swaption volatility
Anurag Gupta, NYU - Case
Liquidity Price Relationship
0.1
0.08
0.05
0
-0.05
-0.04
0.2
Rel BAS
0.3
0.4
0.04
0.04
0
0.1
0.09
EIV
0.12
EIV
EIV
0.15
0
10 year caps/floors
5 year caps/floors
2 year caps/floors
-0.01
-0.06
0
0.04
0.08
0.12
0.16
0
0.04
Rel BAS
 Illiquid options appear to be more “expensive”
Anurag Gupta, NYU - Case
0.08
Rel BAS
0.12
0.16
Liquidity Price Relationship
 Estimate a simultaneous equation model using 3-stage
least squares (liquidity and price may be endogenous)
EIV  c1  c 2 * RelBAS  c3 * LMR  c 4 * LMR 2  c5 * 1LMR0.LMR  
c6SwpnVol  c7 * DefSprd  c8 * 6 Mrate  c9 * Slope
RelBAS  d 1  d 2 * EIV  d 3 * LMR  d 4 * LMR 2  d 5 * 1LMR0.LMR  
d 6*SwpnVol  d 7 * DefSprd  d 8 * LiffeVol  d 9 * CpTbSprd
 First consider only near-the-money options (LMR
between -0.1 and 0.1)
 Instruments for both liquidity and price (Hausman tests
to confirm that variables are exogenous)
Anurag Gupta, NYU - Case
Liquidity Price Relationship
 c2 and d2 are positive and significant for all
maturities (table 3)
 More liquid options are priced lower, while less liquid
options are priced higher, controlling for other effects
 Results hold up to several robustness tests
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Bid and ask prices separately
Two alternative volatility benchmarks
Options across all strikes (include controls for skewness and
kurtosis in the interest rate distribution)
Changes in liquidity change option prices
This result is the opposite of those reported for
other asset classes!
Anurag Gupta, NYU - Case
Economic Significance
 EIVs increase by 25-70 bp for every 1% increase in
relative bid-ask spreads
 One s.d. shock to the liquidity of a cap/floor translates
to an absolute price change of 4%-8% for the
cap/floor
 Longer maturity options have a stronger liquidity
effect
 Higher EIVs when:
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Interest rates are higher
Interest rate uncertainty is higher
 Lower BAS when LIFFE futures volume is higher
(more demand for hedging interest rate risk)
Anurag Gupta, NYU - Case
Contributions
 Contrary to existing findings for other assets, we
document a negative relationship between liquidity
and price – conventional intuition doesn’t always hold
 The pricing of liquidity risk in derivatives should
account for the nature of relationship between
liquidity and derivative prices
 Estimation of liquidity risk for fixed income option
portfolios – GARCH models could be useful
Anurag Gupta, NYU - Case