Tehran Stock Exchange Total Index Modeling by Stochastic Differential Equation

In this paper, efforts have been made so the suitable stochastic differential equation for Tehran Stock Exchange total index modeling to be chosen meticulously. To do so, first the necessity of stochastic models and derived stochastic calculus methods are explained, then the most important stochastic equations in finance (including geometric Brownian motion, model with jump term, nonlinear GARCH, variance-gamma model, Vasicek and Heston) are illustrated. Then the suitable model is selected using a practical approach and considering capability of each model to estimate value at risk and prediction of total index by Monte Carlo simulation method.
Back test’s and fitness function’s results show that the model with a jump term is the most suitable one for value at risk calculation and nonlinear GARCH model is best for prediction of Tehran Stock Exchange total index