The distribution of speculative price changes
Abstract
Most financial models are derived under the i.i.d. normality assumption of price changes, yet past research found the distribution of daily price changes is not normal but leptokurtic. The observed leptokurtosis gives biased results for statistical tests which assume normality, and may explain inaccurate predictions of Black and Scholes' option pricing model. Past research has also shown that daily price changes are not independent. The variance of the distribution is changing over time, which also violates the assumptions of standard option pricing models and the use of standard statistical tests. In order to develop more precise models and statistical tests, the correct distribution of returns must first be determined. To help determine the correct return generating processes for daily futures, cash, exchange rates and stock returns, this research tests the mixed diffusion-jump, extended GARCH models and deterministic chaos. The study is by far the most comprehensive to date, in terms of both the models and the data considered. Daily returns for the assets considered in the present study are not normal with most having fatter tails than a normal distribution. Many of the returns are also skewed. In addition, the i.i.d. assumption is rejected for all cases, the returns are clearly not independent. Of all the models considered, the GARCH(1,1)-t process is the closest to fitting the data. This model reduces leptokurtosis as well as serial dependence considerably. But, Kolmogorov-Smirnov test of fit rejects the GARCH(1,1)-t process for all cases. The standardized residuals are still leptokurtic and skewed, but the nonlinear dependence is removed for much of the data. The GARCH process is shown to provide a considerable improvement over the i.i.d. normal model. The findings of this study suggest the validity of stochastic option pricing models. However, the stochastic model should incorporate the empirical finding of conditional non-normality. All currently available stochastic option pricing models assume normality. The results also suggest the need for further development of random-beta asset pricing models. Tests of the efficient market hypothesis and technical trading systems should account for nonlinear dependence. Finally, statistical tests must adjust for heteroskedasticity in order to be valid.
Degree
Ph.D.
Advisors
Brorsen, Purdue University.
Subject Area
Agricultural economics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.