Review of Quantitative Finance and Accounting, 12 (1999): 327±340
# 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
On the Validity of the Wiener Process Assumption in
Option Pricing Models: Contradictory Evidence
Dean, School of Management, Chaoyang University of Technology
EVA C. YEN
Associate Professor, Department of Business Administration, National Central University
Abstract. This study tests the validity of the critical assumption underlying the option pricing model that the
log form of the stock price movements follows the Wiener process, i.e., stock price movements follow a
geometric Brownian motion.
Using data compiled from the Taiwan Stock Exchange (TSE), this study's major empirical ®ndings are as
follows: ®rst, the null hypothesis that the log of the stock prices is normally distributed is rejected; second, the null
hypothesis that the stock price in log form has mean ln P
t and variance at is rejected; third, the
null hypothesis that successive non-overlapping increments of the log of the stock price are independent from
each other is also rejected. These empirical ®ndings undermine the validity of the Wiener process assumption
which is fundamental to many option pricing models.
Key words: Black and Scholes formula, Wiener Process
JEL Classi®cation: G13, Contingent Pricing
Following Black and Scholes (1973), we have witnessed rapidly growing research
interests in the option pricing models and their wide applications.
In their celebrated
paper, Black and Scholes developed their option pricing model based on the following
(a) The short-term interest rate is known and is constant through time.
(b) The stock price follows a random walk in continuous time with the variance rate
proportional to the square of the stock price. Thus the distribution of possible stock
prices at the end of any ®nite interval is lognormal with the variance rate being
(c) The stock pays no dividends.
(d) The option is ``European'', that is, it can only be exercised at maturity.
(e) There are no transaction costs in buying or selling the stock or the option.
(f ) It is possible to borrow any amount of money at the short-term interest rate.