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BidAsk Spreads: A Comparative Analysis

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Apply models of spread to compare costs/benefits of different trading structures ... Jameson and Wilhelm (1992) - absolute quoted spread function of: ... – PowerPoint PPT presentation

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Title: 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 (/--)

7
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 ()

9
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 ()

10
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.

11
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.
17
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.

18
Inventory-holding premium
  • Perfect hedge is not possible because of trading
    costs in stocks or stock options market because
    of high trading costs.

19
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

20
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.

22
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.

23
Simulation of IHP
  • IHP as a function of time between trades and
    volatility.

24
Model specification
  • Expect
  • Intercept to be minimum tick size.
  • Coefficient on IHP to be positive.
  • Coefficient on InvTV to be fixed costs.

25
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.

26
Stock spreads
  • Descriptive statistics

27
Stock spreads
  • Correlation structure

28
Stock spreads
 
 
  • Regression results

29
Option spreads
 
 
  • Descriptive statistics

30
Option spreads
 
 
  • Descriptive statistics

31
Option spreads
 
 
  • Equal-weighted quoted spreads

32
Option spreads
 
 
  • Volume-weighted effective spreads

33
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.

35
Model specification
 
 
 
 
 
Benchmark model
36
Model specification
 
 
 
 
 
  • Regression results - EWQS

37
Model specification
 
 
 
 
 
  • Regression results - VWES

38
Model specification
 
 
 
 
 
  • Results appear to be influenced by other factors.
  • Use deFontnouvelle (2003) et al dummies for
    maximum spread categories.

39
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.

40
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.
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