Liquidity Effects in Interest Rate Options Markets: Premium or Discount?Prachi DeuskarAnurag GuptaMarti G. Subrahmanyam

ObjectivesHow 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)

Related Literature Equity MarketsIlliquid / higher liquidity risk stocks have lower prices (higher expected returns)Amihud and Mendelsen (1986), Pastor and Stambaugh (2003), Acharya and Pedersen (2005), and many othersSignificant commonality in liquidity across stocksChordia, Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), Huberman and Halka (2001), Amihud (2002), and many others

Related Literature Fixed Income MarketsIlliquidity affects bond prices adverselyAmihud and Mendelsen (1991), Krishnamurthy (2002), Longstaff (2004), and many othersMore recent papers include Chacko, Mahanti, Mallik, Nashikkar, Subrahmanyam (2007) and Mahanti, Nashikkar, Subrahmanyam (2007)Common factors drive liquidity in bond marketsChordia, Sarkar, and Subrahmanyam (2003), Elton, Gruber, Agarwal, and Mann (2001), Longstaff (2005), and many others

Related Literature Derivative MarketsRelatively little is knownVijh (1990), Mayhew (2002), Bollen and Whaley (2004) present some evidence from equity optionsBrenner, Eldor and Hauser (2001) report that non-tradable currency options are discountedLongstaff (1995) and Constantinides (1997) present theoretical arguments why illiquid options should be discounted

How should illiquidity affect asset prices?Negatively, as per current literatureConventional wisdom: More illiquid assets must have higher returns, hence lower pricesThe buyer of the asset demands compensation for illiquidity, while the seller is no longer concerned about liquidityTrue 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?

How should liquidity affect derivative prices?Derivatives are generally in zero net supplyRisk 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 transactionThe buyer would demand a reduction in price, while the seller would demand an increase in priceIf 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

How should illiquidity affect interest rate option prices?Caps/floors are long dated OTC contractsMostly institutional marketSellers are typically large banks, buyers are corporate clients and some smaller banksCustomers are usually on the ask-sideBuyers typically hold the options, as they may be hedging some underlying interest rate exposuresSellers are concerned about their risk exposures, so they may be more concerned about the liquidity of the options that they have soldMarginal investors likely to be net short

Unhedgeable Risks in OptionsLong dated contracts (2-10 years), so enormous transactions costs if dynamically hedged using the underlyingDeviations 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

Upward Sloping Supply Curve Since some part of option risks is unhedgeableOption liquidity related to the slope of the supply curveIlliquidity makes it difficult for sellers to reverse trades have to hold inventory (basis risk)Model risk fewer option trades to calibrate modelsHence supply curve is steeper when there is less liquidityWider bid-ask spreadsHigher prices, since dealers are net short in the aggregate

DataEuro 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 quotesNine maturities (2-10 years) across twelve strikes (2%-8%) not all maturity strike combinations available each dayOptions on the 6-month Euribor with a 6-month resetAlso obtained Euro swap rates and daily term structure data from WestLB

Sample Data (basis point prices)

Data TransformationStrike to LMR (Log Moneyness Ratio) logarithm of the ratio of the par swap rate to the strike rate of the optionEIV (Excess Implied Volatility) difference between the IV (based on mid-price) and a benchmark volatility using a panel GARCH modelUsing IV removes term structure effectsSubtracting a benchmark volatility removes aggregate variations in volatilityHence its a measure of expensiveness of optionsUseful for examining factors other than term structure or interest rate uncertainty that may affect option prices

Scaled bid-ask spreads (Table 2)

Panel GARCH Model for Benchmark VolatilityPanel 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

Liquidity Price Relationship

Illiquid options appear to be more expensive

Liquidity Price RelationshipEstimate 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)

Liquidity Price Relationshipc2 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 effectsResults hold up to several robustness testsBid and ask prices separatelyTwo alternative volatility benchmarksOptions 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!

Economic SignificanceEIVs increase by 25-70 bp for every 1% increase in relative bid-ask spreadsOne s.d. shock to the liquidity of a cap/floor translates to an absolute price change of 4%-8% for the cap/floorLonger maturity options have a stronger liquidity effectHigher EIVs when:Interest rates are higherInterest rate uncertainty is higherLower BAS when LIFFE futures volume is higher (more demand for hedging interest rate risk)

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

Extracting the common liquidity factorPanel regression (9 maturities, 3 moneyness buckets each)

Include panel fixed effectsDisturbances:HeteroskedasticPotentially correlated across panelsSerially correlated within panels (AR(1))Prais-Winsten full FGLS estimationRe-estimate using alternative error structures and estimation methods for robustnessc2 is positive, Adj R2 of 9% (44,070 observations)

Extracting the common liquidity factorExamine the principal components of the residuals of the panel regressionFirst factor explains 33% - suggests a market-wide systematic component to these liquidity shocksParallel shock across all maturities and strikes higher loading on OTM and ATM optionsSecond 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

Macro-economic drivers of Common Liquidity FactorConstruct a daily (unexplained) systematic liquidity factor based on the residuals and the first principal componentRegress this factor on contemporaneous and lagged changes in macro-economic variablesShort rate and slope of the term structure do not appear to heave any effect on this factorDefault spread not related as well dealers are mostly on the sell sideUncertainties in fixed income and equity markets appear to drive this systematic liquidity factor, with a lag of 1-4 days

ContributionsContrary to existing findings for other assets, we document a negative relationship between liquidity and price conventional intuition doesnt always holdA significant common factor drives changes in liquidity in this options marketChanges in uncertainty in fixed income and equity markets drive this common liquidity factor

Implications of our StudyEstimation of liquidity risk for fixed income option portfolios GARCH models could be usefulHedging liquidity risk in fixed income option portfolios could form macro-hedges using equity and fixed income optionsMacro-economic drivers of liquidity provide some guidelines for including liquidity as a factor in fixed income option pricing models