Liquidity Effects in Interest Rate Options Markets: Premium or Discount? Prachi Deuskar Anurag Gupta Marti G. Subrahmanyam

Anurag Gupta, Case Western Reserve University Objectives How does illiquidity affect option prices? What drives liquidity in option markets? We study these two questions in the Euro interest rate options markets (caps/floors)

Anurag Gupta, Case Western Reserve University 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 Significant commonality in liquidity across stocks Chordia, Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), Huberman and Halka (2001), Amihud (2002), and many others

Anurag Gupta, Case Western Reserve University 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 (2007) and Mahanti, Nashikkar, Subrahmanyam (2007) Common factors drive liquidity in bond markets Chordia, Sarkar, and Subrahmanyam (2003), Elton, Gruber, Agarwal, and Mann (2001), Longstaff (2005), and many others

Anurag Gupta, Case Western Reserve University 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, Case Western Reserve University 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, Case Western Reserve University 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, Case Western Reserve University How should illiquidity affect interest rate 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, Case Western Reserve University 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, Case Western Reserve University 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, Case Western Reserve University 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, Case Western Reserve University Sample Data (basis point prices)

Anurag Gupta, Case Western Reserve University 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, Case Western Reserve University Scaled bid-ask spreads (Table 2)

Anurag Gupta, Case Western Reserve University 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, Case Western Reserve University Liquidity Price Relationship Illiquid options appear to be more “expensive”

Anurag Gupta, Case Western Reserve University 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, Case Western Reserve University 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, Case Western Reserve University Economic Significance EIVs increase by 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, Case Western Reserve University Are there common drivers of liquidity? Compute average correlations between RelBAS within moneyness buckets across maturities (table 9) Some part of the variation appears to be systematic

Anurag Gupta, Case Western Reserve University Extracting the common liquidity factor Panel regression (9 maturities, 3 moneyness buckets each) Include panel fixed effects Disturbances: Heteroskedastic Potentially correlated across panels Serially correlated within panels (AR(1)) Prais-Winsten full FGLS estimation Re-estimate using alternative error structures and estimation methods for robustness c2 is positive, Adj R 2 of 9% (44,070 observations)

Anurag Gupta, Case Western Reserve University Extracting the common liquidity factor Examine the principal components of the residuals of the panel regression First factor explains 33% - suggests a market-wide systematic component to these liquidity shocks Parallel shock across all maturities and strikes – higher loading on OTM and ATM options Second factor explains 11% (others insignificant) Negative weight on OTM options, positive weight on ATM/ITM options (more positive on ITM options) Substitution effect – demand may partially shift away from ATM/ITM options to OTM options when the market is hit by the second type of common liquidity shock

Anurag Gupta, Case Western Reserve University Macro-economic drivers of Common Liquidity Factor Construct a daily (unexplained) systematic liquidity factor based on the residuals and the first principal component Regress this factor on contemporaneous and lagged changes in macro-economic variables Short rate and slope of the term structure do not appear to heave any effect on this factor Default spread not related as well – dealers are mostly on the sell side Uncertainties in fixed income and equity markets appear to drive this systematic liquidity factor, with a lag of 1-4 days

Anurag Gupta, Case Western Reserve University Contributions Contrary to existing findings for other assets, we document a negative relationship between liquidity and price – conventional intuition doesn’t always hold A significant common factor drives changes in liquidity in this options market Changes in uncertainty in fixed income and equity markets drive this common liquidity factor

Anurag Gupta, Case Western Reserve University Implications of our Study Estimation of liquidity risk for fixed income option portfolios – GARCH models could be useful Hedging liquidity risk in fixed income option portfolios – could form macro-hedges using equity and fixed income options Macro-economic drivers of liquidity provide some guidelines for including liquidity as a factor in fixed income option pricing models