A switching model approach to stock price modeling

Abstract

In this study, we consider a nonlinear probabilistic discretized version of Geo- metric Brownian Motion (GBM) to model the stock prices traded in Istanbul Stock Exchange. By nonlinearity we mean the existence of di¤erent states in the model, namely positive return process, negative return process. As the names im- ply, each process is formed using positive and negative returns respectively. The model decides which process to use according to a probabilistic framework en- dogenously determined in the model. By means of these probabilities, this model is designed to give better t than GBM, where the better t is acquired by Mean Squared Errors (MSE). We obtain the results via the Monte Carlo technique using Matlab and hundred stock prices. As a result, the obtained probabilities after simulation demonstrate that positive returns tend to be followed by negative return process and vice versa.