A numerical resolution of a European option value with a stochastic volatility

Abstract

The aim of this work is to evaluate a European option with a stochastic volatility. For, we have a system of two stochastic differential equations (SDEs), where the first one describes the price of the underlying while the second one modelises the stochastic volatility. First we set the inconvenience of Black and Scholes model [1] and its limits, then we propose a model with a stochastic volatility. For this purpose, we use Garman partial differential equation (GPDE) to evaluate the option price where solution is approached by a finite difference method.