An Approximation Scheme for Value at Risk under Mean Reverting Stochastic Volatility Model

Abstract

AbstractIn this paper, a stochastic differential equation is provided for the stock price in which not only the volatility of returns is stochastic same as Hull and White model but also, it has the mean-reverting property. Then, to analyze the probability distribution of this model, the Fokker--Plank equation is applied and the resulting problem is solved numerically. The well known numerical scheme, q-method is applied to approximate the solution of the resulting equation. Finally, a practical application of the provided model in financial aspects is shown within a numerical example. In this example, the proposed model and numerical results are used to approximate the Value at Risk (VaR) of the Tehran stock exchange total index.