Comparison Models of Brownian motion and Fractional Brownian Motion and GARCH in Volatility Estimation of Stock Return

Efficiency volatility modeling in stock markets, as seen by academic people and operators in Finance science, in terms of its application in predicting stock efficiency, is of considerable importance. Financial and capital markets in the country has taken effective stepsto develop.This paper aims to develop a model for estimating and forecasting volatility of stock returns is done in the Tehran Stock Exchange. All three models use data on prices, daily top 50 shooters in a 5-year period from 2008 to 2013, is employed Brownian Motion, Fractional Brownian motion and GARCH models .using Excel and Eviews and MATLAB software was designed with the fractional Brownian model. Tests and comparisons using MSE, RMSE, and MAE were performed. Comparing the results of the model of Brownian motion, fractional Brownian fashion model and GARCH, the GARCH model has identified as a top model.