Numerical approximation for options pricing of a stochastic volatility jump-diffusion model
Résumé
In this paper, we are interested in pricing options (European and Quanto) by a Model in which the asset prices follow a jump-diffusion model with a stochastic volatility in n dimensions. The stochastic volatility also follows the jump-diffusion in d dimensions. We've already stated the existence and uniqueness of the solution of the partial integro-differential equation in the multidimensional case (s = d + n), in a previous study (Aboulaich, Baghery and Jraifi, 2013). The infinitesimal operator associated with the stochastic volatility didn't contain the jumps term. And the numerical approximation was made for the bidimensional case only. The present paper aims to numerically simulate the model when the dimension is greater or equal to 2. At first, we use the Monte Carlo method to compare the numerical results with those of (Xu, Wu and Li, 2011) for s = 4. Then, we show how the convergence speed of the Monte Carlo Method can be improved using a Quasi Monte Carlo Method based on the Halton sequences. For a small dimension (s = 2) we use the finite element method. In order to compare the numerical results, we consider the data and parameters used by (Broadie and Kaya, 2006).