A variable coefficient method for accurate Monte Carlo simulation of dynamic asset price

Abstract

In this work, we propose an adaptive Monte Carlo (MC) simulation technique to compute the sample paths for the dynamical asset price. In contrast to conventional MC simulation with constant drift and volatility (mu,sigma) , our MC simulation is performed with variable coefficient methods for(mu,sigma)in the solution scheme, where the explored dynamic asset pricing model starts from the formulation of geometric Brownian motion. With the method of simultaneously updated (mu,sigma) , more than 5,000 runs of MC simulation are performed to fulfills basic accuracy of the large-scale computation and suppresses statistical variance. Daily changes of stock market index in Taiwan and Japan are investigated and analyzed.