# Presentation: 513197

## Liquidity Effects in Interest Rate Options Markets: Premium or Discount?

- Prachi Deuskar
- Anurag Gupta
- Marti G. Subrahmanyam

## 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)

## 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

## 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

## 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

## 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?

## 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

## 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*

## 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*

## 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

## 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

## Sample Data (basis point prices)

## 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

## Scaled bid-ask spreads (Table 2)

## 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

## Liquidity Price Relationship

- Illiquid options appear to be more “expensive”

## 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)

## 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!***

## 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)

## 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 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 R2 of 9% (44,070 observations)

## 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

## 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

## 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

## 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