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## Liquidity Effect in OTC Options Markets: Premium or Discount?

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**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 • 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 non-tradable 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 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 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 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 • 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 • 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 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)**Anurag Gupta, NYU - Case**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 • 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 • Two alternative benchmarks for robustness: • Simple historical vol (s.d. of changes in log forward rates) • Comparable ATM diagonal swaption volatility Anurag Gupta, NYU - Case**Liquidity Price Relationship**• Illiquid options appear to be more “expensive” Anurag Gupta, NYU - Case**Liquidity Price Relationship**• Estimate a simultaneous equation model using 3-stage least squares (liquidity and price may be endogenous) • 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 • 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: • 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