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

The aim of this work is to evaluate a European option with a stochas-tic volatility. For, we have a system of two stochastic dierential equa-tions (SDEs), where the rst one describes the price of the underlyingwhile the second one modelises the stochastic volatility. First we setthe inconvenience of Black and Scholes model [1] and its limits, thenwe propose a model with a stochastic volatility. For this purpose, weuse Garman partial dierential equation (GPDE) to evaluate the optionprice where solution is approached by a nite dierence method.