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• So there will be a simultaneous relationship.
29 30 The Data • All trading days during 1989 are used for observations.
• The average bid & ask prices are calculated for each option
during the time 2:00pm – 2:15pm Central Standard time.
• The following are then dropped from the sample for that day:
1. Any options that do not have bid / ask quotes reported
during the ¼ hour.
2. Any options with fewer than 10 trades during the day.
• The option price is defined as the average of the bid & ask.
• We get a total of 2456 observations. This is a pooled
31 The Models • For the calls:
(2) • And symmetrically for the puts:
where PRi & CRi are the squared deltas of the options 32 The Models (cont’d)
• CDUMi and PDUMi are dummy variables
if Ci or Pi < $3
if Ci or Pi ≥ $3 • T2 allows for a nonlinear relationship between time to maturity and the
spread. • M2 is used since ATM options have a higher trading volume. • Aside: are the equations identified? • Equations (1) & (2) and then separately (3) & (4) are estimated using
33 Results 1 34 Results 2 35 Comments: Adjusted R2 ≈ 60% α1 and β1 measure the tick size constraint on the spread
α2 and β2 measure the effect of the option price on the spread
α3 and β3 measure the effect of trading activity on the spread
α4 and β4 measure the effect of time to maturity on the spread
α5 and β5 measure the effect of risk on the spread
γ1 and δ1 measure the effect of the spread size on trading activity
etc. 36 Calls and Puts as Substitutes • The paper argues that calls and puts might be viewed as
substitutes since they are all written on the same
• So call trading activity might depend on the put spread and
put trading activity might depend on the call spread.
• The results for the other variables are little changed. 37 Conclusions
• Bid - Ask spread variations between options can be explained
by reference to the level of trading activity, deltas, time to
maturity etc. There is a 2 way relationship between volume
and the spread.
• The authors argue that in the second part of the paper, they did
indeed find evidence of substitutability between calls & puts.
- No diagnostics.
- Why do the CL and PL equations not contain the CR and PR
- Could have tested for endogeneity of CBA and CL.
- Why are the squared terms in maturity and moneyness only
in the liquidity regressions?
- Wrong sign on the squared deltas.
38 Vector Autoregressive Models • A natural generalization of autoregressive models is popularized by Sims • A VAR is in a sense a system of regression model, i.e., there is more than
one dependent variable. • Simplest case is a bivariate VAR where uit is an iid disturbance term with E(uit)=0, i=1,2; E(u1t u2t)=0.
• The analysis could be extended to a VAR(g) model, or so that there are g
variables and g equations. 39 Vector Autoregressive Models:
Notation and Co...
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