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 findings are as follows: first, 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 s + (µ- \( - \frac{1}{2}\) σ2)t] and variance αt 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 findings undermine the validity of the Wiener process assumption which is fundamental to many option pricing models.
Similar content being viewed by others
References
Bachelier, L., ``Theory of Speculation (English translation).'' in P.H. Cootner, ed., The Random Character of Stock Market Prices, MIT Press, Cambridge, Mass., 17-78, 1900.
Ball, C. and A. Roma, ``Stochastic Volatility Option Pricing.'' Journal of Financial and Quantitative Analysis 4, 589-607, (1994).
Black, F. and M. Scholes, ``The Pricing of Options and Corporate Liabilities.'' Journal of Political Economy 81, 637-669, (1973).
Black, F., ``Fact and Fantasy in the Use of Options.'' Financial Analysts Journal 31, 36-41, 61-72, (1975).
Black, F., ``How to Use the Holes in Black-Scholes.'' in D. Chew, ed., The New Corporate Finance: Where Theory Meets Practice, McGraw-Hill, New York, 419-425, 1993.
Cox, J.C. and S.A. Ross, ``The Valuation of Options for Alternative Stochastic Processes.'' Journal of Financial Economics 3, 145-166, (1976).
Cox, J.C., M. Rubinstein, and S. Ross, ``Option Pricing: A Simpli®ed Approach.'' Journal of Financial Economics 7, 229-263, (1979).
Fujihara, R. and K. Park, ``The Probability Distribution of Futures Prices in the Foreign Exchange Market: A Comparison of Candidate Processes.'' Journal of Futures Markets 6, 623-641, (1990).
Hall, J.A., B.W. Brorsen, and S.H. Irwin, ``The Distribution of Futures Prices: A Test of Stable Paretian and Mixture of Normal Hypotheses.'' Journal of Financial and Quantitative Analysis 24, 105-116, (1989).
Huang, Chi-fu, ``Contingent Securities Valuation in Continuous Time.'' Journal of Financial Studies, The Chinese Finance Association, 2, 127-143, (1994).
Hudson, M.A., R.M. Leuthod, and G.P. Sarassoro, ``Commodity Futures Price Changes: Recent Evidence for Wheat, Soybean and Live Cattle.'' Journal of Futures Markets 7, 287-301, (1987).
Jackwerth, J.C. and M. Rubinstein, ``Recovering Probability Distributions from Option Prices.'' The Journal of Finance 51, 1611-1631, (1996).
Kang, T. and B.W. Brorsen, ``Conditional Heteroskedasticity, Asymmetry and Option Pricing.'' Journal of Futures Markets 8, 901-928, (1983).
Lee, C.F., G. Yen, and C. Chang, ``Informational Ef®ciency of Capital Market Revisited: Anomalous Evidence from A Re®ned Test.'' Advances in Quantitative Analysis of Finance and Accounting 2(A), 39-65, (1993).
Merton, R.C., ``Theory of Rational Option Pricing.'' Bell Journal of Economics and Management Science 4, 141-183, (1973).
Merton, R.C., ``Option Pricing: When Underlying Stock Returns are Discontinuous.'' Journal of Financial Economics 3, 125-144, (1976).
Papoulis, A., Probability, Random Variables, and Stochastic Process, 3rd ed., McGraw-Hill, New York, 1991.
Roll, R., ``An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends.'' Journal of Financial Economics 5, 251-258, (1977).
Samuelson, P., ``Rational Theory of Warrant Pricing.'' Industrial Management Review 6, 13-32, (1965).
Smith, C.W. Jr., ``Option Pricing: A Review.'' in J.C. Francis, C.F. Lee, and D.E. Farrar, eds., Readings in Investments, McGraw-Hill, New York, 616-664, 1976.
Taylor, S.J., ``The Behavior of Futures Return over Time.'' Applied Economics 17, 713-734, (1985).
Yang, S.R. and B.W. Brorsen, ``Nonlinear Dynamics of Daily Futures Price: Conditional Heteroskedasticity or Chaos.'' Journal of Futures Markets 13, 175-191, (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yen, G., Yen, E.C. On the Validity of the Wiener Process Assumption in Option Pricing Models: Contradictory Evidence from Taiwan. Review of Quantitative Finance and Accounting 12, 327–340 (1999). https://doi.org/10.1023/A:1008309307499
Issue Date:
DOI: https://doi.org/10.1023/A:1008309307499