Review of Quantitative Finance and Accounting, 9 (1997): 269–288
© 1997 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
On the Distribution of CBOE Option Trade Prices
Occurring Between Consecutive Stock Trades
Associate Professor of Accounting at Feng-Chia University in Taiwan.
Professor of Finance at Brock University in St. Catharines, Ontario.
Professor of Accounting at Fu Jen University in Taiwan.
Abstract. This paper examines the volume distribution of option trade prices that occurs when the underlying
stock price remains constant. The width of these option trade price bands provides direct evidence on the law of
one price and the redundancy of options assumed in many option models. We ﬁnd that index option bands are
narrower than equity option bands. Furthermore, for both equity and index options, puts have narrower band-
widths than calls. In general, option price bandwidth is narrow and can be explained by the minimum price
movement allowed by the Chicago Board Options Exchanges (CBOE). This supports the single price law and the
redundancy assumption. The existence of bid/ask quotes on the option does not materially affect the above
results although it does alter the frequency of multiple option trade prices for a given underlying stock price. We
note that over 53% of option trading volume occurs without bid/ask quotes on the CBOE compared to less than
15% a decade ago. Our results suggest that the effective bid/ask spread on options is probably no larger than the
minimum price movements allowed by the CBOE. Furthermore, the need for the liquidity services of market
makers may be declining if the decline in quoting activity stems from cross trading (i.e. trades not involving
Key words: distribution of CBOE option trade prices
In the Berekely Options Data Base which reports all trades and quotes on the Chicago
Board Options Exchange (CBOE), it is common to observe more than one option trade
price during an interval when the stock price does not change from its last trade price
(hereafter a constant stock price interval or CSPI). For example in the three years
(1987–9) of this study we ﬁnd multiple trade prices represent nearly 36% of equity call
option volume for CSPIs with at least one bid/ask quote. As Rubinstein (1985) notes, this
causes confusion about the equilibrium option price for a given stock price. Furthermore,
Chen and Welch  point out this situation could challenge the law of one price if
options are redundant securities.
They postulate that if the dispersion of option trade
prices is wider than any reasonable effective bid/ask spread,
this can be viewed as
evidence against the redundancy of options or a violation of the law of one price. The
former violation implies other stochastic variables are changing during the CSPI while the
@ats-ss11/data11/kluwer/journals/requ/v9n3art3 COMPOSED: 09/16/97 2:11 pm. PG.POS. 1 SESSION: 10