In table 4.7, we regress the violation of put-call parity (the deviation of
the synthetic stub) on the actual stub for Palm and Stratos. For Palm, the
synthetic stub deviation moves strongly with the actual stub, and even
with just nineteen weekly observations, we can reject the hypothesis that
the two do not move together. The R^2 is a whopping .96, suggesting that
violations of put-call parity are strongly related to apparent near-arbitrage
opportunities. For Stratos, the R^2 is lower at .70, but again we can easily
reject the hypothesis that the stub and the deviation of actual from synthetic
are unrelated.
Are these violations of put-call parity unusual? Most empirical studies of
options prices have found that put-call parity basically holds, with small or
fleeting violations due perhaps to trading costs or asynchronous price data
(Klemkosky and Resnick 1979, Bodurtha and Courtadon 1986). One
might wonder whether put-call parity generally holds using data from our
sample period and using our sources and methods. Although a thorough in-
vestigation of put-call parity for all equity options is beyond the scope of
this chapter, we did do a brief check as follows. We picked a random date,
October 10, 2000, and compared the synthetic short on Stratos with those
of other options. Stratos options started trading on the Chicago Board
Options Exchange (CBOE) on July 12, 2000. We looked at 28 other firms
in which options were initially listed on the CBOE between June 11 and
July 12, 2000. Most of these firms were, like Stratos, recent technology
158 LAMONT AND THALER
Table 4.7
Regression of Synthetic Stub Deviation on Actual StubPalm Stratos
Constant −8.15 −5.95
(.24) (.50)
St .50 .83
(.02) (.08)
Observations 19 42
R^2 .96 .71
Note.The dependent variable is the deviation between the actual
stub and the synthetic stub, expressed in dollars per parent share.
The actual stub, Stuses actual prices of the shares. The synthetic
stub uses the actual price of parent shares and the synthetic short
price of subsidiary shares. The synthetic short price is constructed
by selling a six-month at-the-money call at the bid prices, buying a
six-month at-the-money put at the ask prices, and borrowing the
present value of the exercise price at the six-month LIBOR rate.
The regression for Palm uses 19 weekly observations as of Friday
March 17, 2000–July 21, 2000; the regression for Stratos uses 42
weekly observations as of Friday July 14, 2000–April 27, 2001