Modeling of Tehran Stock Exchange Overall Index by Heston Stochastic Differential Equation

Abstract

In this study, overall index of Tehran Stock Exchange is modeled by Heston stochastic differential equations and its performance is measured. To do this, after a brief introduction of stochastic differential equations, Heston model is explained in more detail and parameters of this model based on the data of Tehran Stock Exchange overall index is estimated. In this way, Fokker-Plank theorem is used to find probability distribution function of Heston model and Gauss-Hermit method is used to estimate an indefinite integral. Finally we calculate value at risk of Tehran Stock Exchange overall index by Monte Carlo methods based on Heston model and we compare this with Geometric Brownian model as a widely used model by means of back test approach. These tests show superior performance of Heston model.

Keywords

• Keywords: Stochastic Differential Equations; Heston Model; Fokker–Planck Equation; Gauss-Hermite Method; Value at Risk