Liquidity Effects in Interest Rate Options Markets: Premiu

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Liquidity Effects in Interest Rate Options
Markets Premium or Discount?

• Prachi Deuskar
• Anurag Gupta
• Marti G. Subrahmanyam

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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)

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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

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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

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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

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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?

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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

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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

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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

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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

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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

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Sample Data (basis point prices)
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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 its a measure of expensiveness of
  options
• Useful for examining factors other than term
  structure or interest rate uncertainty that may
  affect option prices

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Scaled bid-ask spreads (Table 2)
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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

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Liquidity Price Relationship

• Illiquid options appear to be more expensive

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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)

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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!

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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)

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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

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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)

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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

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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

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Contributions

• Contrary to existing findings for other assets,
  we document a negative relationship between
  liquidity and price conventional intuition
  doesnt 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

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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