BidAsk Spreads: A Comparative Analysis

1
Bid/Ask Spreads A Comparative Analysis

• Nicolas Bollen, Vanderbilt University
• Hans R. Stoll, Vanderbilt University
• Robert E. Whaley, Duke University

2
Background

• Two types of studies of market maker spreads
• Develop and test theoretical models of spreads
  determinants.
• Pioneering work by Demsetz (1968).
• Stoll (2003) provides comprehensive review.

3
Background

• Two types of studies of market maker spreads
• Apply models of spread to compare costs/benefits
  of different trading structures or assess effects
  of intervention.
• Tinic and West (1974) agent vs dealer-dominated
  markets.
• Bacidore (1997) decimalization
• Bessembinder (1999) order-processing rules

4
Background

• With few exceptions, models of spreads and policy
  examinations have focused on stock market.
• Most actively-traded corporate security.
• Long histories of exchange trade and quote data
  available.

5
Background

• Some studies have focused on stock option market
  to assess effects of multiple listing.
• Neal (1987) Difference in spreads of AMEX
  options in 1985 and 1986.
• Mayhew (2002) Difference in spreads of CBOE
  options in 1986 to 1997.
• De Fontnouvelle et al (2003) Reduction in
  spreads during August 1999 when competition among
  exchanges was unleashed.
• Battalio et al (2003) shows reduction in spreads
  in recent years due to competition.

6
Background

• Studies have not agreed on an appropriate
  structural model.
• Neal (1987) - absolute quoted spread function of
• Trading volume (--)
• Option price ()
• ISD times elasticity (/--)

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Background

• Studies have not agreed on an appropriate
  structural model.
• Jameson and Wilhelm (1992) - absolute quoted
  spread function of
• ISD2 times elasticity2 times stock price ()
• Gamma ()
• Vega ()
• Abs(1-PVX/S) ()
• Elasticity ()

8
Background

• Studies have not agreed on an appropriate
  structural model.
• de Fontnouvelle et al (2003) - absolute effective
  spread function of
• Trading volume (--)
• Option price ()
• Delta (/--)
• Gamma (/-)
• ISD ()
• Stock spread ()

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Background

• Studies have not agreed on an appropriate
  structural model.
• Battalio et al (2003) - absolute effective spread
  function of
• Inverse of option price (--)
• Stock volatility (ln of high/low) ()
• Ln of market cap (-)
• Trade size ()

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Purpose of research

• Develop and test new model of bid/ask spread for
  stock options.
• Simple and parsimonious structural form.
• Supported empirically.
• Use model to compare and analyze differences
  between stock and stock option spreads.

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Outline

• Describe option price dynamics
• Introduce concept of inventory-holding premium
  (IHP)
• Apply concept to stock spreads
• Extend model to stock option spreads
• Examine estimation results
• Discuss planned future work

12
Model development

• Determinants of option value

13
Model development

• Approximate change in option value through time.

14
Model development

• Approximate change in option value through time.

15
Model development

• Can hedge delta, gamma, and vega risks using
  other securities.
• Total cost of hedge is sum product of number of
  each security bought/sold and its bid/ask spread.

16
Model development

• Can hedge delta, gamma, and vega risks using
  other securities.

E.g., use delta times stock spread as cost of
delta-hedging option.
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Issues

• Motivates use of delta, gamma, and vega in
  regression model.
• Hedging costs on a series-by-series basis would
  be prohibitive.
• Reduced by the fact the market maker hedges at a
  portfolio level.
• Nonetheless, incremental hedging costs are likely
  to be related to risk measures.

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Inventory-holding premium

• Perfect hedge is not possible because of trading
  costs in stocks or stock options market because
  of high trading costs.

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Inventory-holding premium

• Assume market maker sets bid/ask spread so as to
  be compensated for expected adverse price
  movements.
• Suppose market is long risk is that price will
  fall while security is in inventory, i.e.,
• Expected loss conditional on a loss occurring
  times probability of loss occurring is

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Inventory-holding premium

• This inventory-holding premium
• has value

21
Inventory-holding premium

• Note functional form.
• IHP is nonlinear function of
• share price (S)
• return volatility (s)
• market makers holding period (t)
• Entering variables separately obfuscates their
  role.

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Simulation of IHP

• Assume
• Stock price is 27.50 a share
• Volatility rate ranges from 0 to 100.
• Number of minutes between offsetting trades
  ranges from 0 to 20.

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Simulation of IHP

• IHP as a function of time between trades and
  volatility.

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Model specification

• Expect
• Intercept to be minimum tick size.
• Coefficient on IHP to be positive.
• Coefficient on InvTV to be fixed costs.

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Data

• CBOE stock options listed on 16 NYSE stocks
  during February 2001.
• Most active option classes (50,000 contracts
  traded during month).
• Both options and underlying stocks trade in
  decimals.

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Stock spreads

• Descriptive statistics

27
Stock spreads

• Correlation structure

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Stock spreads
 
 

• Regression results

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Option spreads
 
 

• Descriptive statistics

30
Option spreads
 
 

• Descriptive statistics

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Option spreads
 
 

• Equal-weighted quoted spreads

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Option spreads
 
 

• Volume-weighted effective spreads

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Model specification

• Separate IHPs for each source of risk. E.g.,

34
Model specification

• Expect
• Intercept to be minimum tick size.
• Coefficients on IHPs to be positive.
• Coefficient on InvTV to be fixed costs.
• Coefficient on 3 dummy to be five cents.

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Model specification
 
 
 
 
 
Benchmark model
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Model specification
 
 
 
 
 

• Regression results - EWQS

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Model specification
 
 
 
 
 

• Regression results - VWES

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Model specification
 
 
 
 
 

• Results appear to be influenced by other factors.
• Use deFontnouvelle (2003) et al dummies for
  maximum spread categories.

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Summary

• Project is incomplete.
• Develop simple, parsimonious model for option
  spread.
• Permits understanding why previous regression
  models performed well, even though their
  specifications varied.
• Works better than competing models, but does not
  explain why option price effect.

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Summary

• Next steps.
• Examine more recent periods.
• Given increased competition, price effect may
  have become smaller.
• Also, need to develop a more accurate proxy for
  length of market makers expected holding period.
• Once problems are overcome, estimate spread model
  across stock and stock spreads simultaneously.
• Isolate differences in cost components.