Stock Price Modeling and Forecasting Using Stochastic Differential Equations

Time series processes can be classified to three models, linear models, stochastic models and chaotic models. Based on this classification the linear models are forecast able, the stochastic models are unforecastable and the chaotic models are semi forecast able. The previous researches in the modeling and forecasting of the stock price usually try to prove that, the fluctuations of the share prices in Tehran Stock Exchange are not random walks in spite of the existence similarity to the random walks. Indeed the market has a chaotic behavior. This means that, the Efficient Market Hypothesis (EMH) is failed. Therefore by using a complex and powerful models such as artificial neural networks, one can forecast stock prices in Tehran stock market. This paper proposed another approach to modeling and forecasting of the share price. This approach is based on the Stochastic Differential Equations. The modeling is based on the Black- Scholes pricing model. Comparison the simulation result with the linear ARIMA model indicates that the proposed structure provides an accurate next step and the long term share prices and daily returns forecasting.