Brownian Motion Model With Stochastic Parameters For Asset Prices

The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift mu and volatility sigma may change over time. Presently we consider a model in which the parameter x = (mu,sigma) is such that its value x (t + Delta t) at a short time Delta t ahead of the present time t depends on the value of the asset price at time t + Delta t as well as the present parameter value x(t) and m(-1) other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.