Modeling of Stock Markets with Mean Reversion

In this article we present a method for modeling and estimating the stock market with a mean reverting characteristic. Mean reversion is the tendency for the market to move back to an equilibrium level. The random walk description of stock markets has certain inaccuracies as such a process may diverge over time, resulting in negative or infinite values. There is no longer an acceptable model which can be effectively used to simulate the stock market. However, the mean reverting property exhibited by financial markets has been recognized by theorists. We analyze two methods of estimating the parameters of the model, Least Square Estimation and Maximum Likelihood Estimation. Using monthly data of the Dow Jones Industrial Average and the Singapore Straits Times Index, we compare the performance of these two methods.