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Option pricing for a stochastic volatility jump-diffusion model

R. Aboulaich, F. Baghery, A. Jraifi

Abstract


In this work, we consider the jump diffusion model with a stochastic volatility for option pricing. We use a variational formulation in an appropriate weighted space in order to numerically solve the problem via the finite element method. An existence and uniqueness results are established in (Zhang, 1997) for a one-dimensional Levy measure and constant
volatility. In this paper we generalize the result for a multidimensional Levy measure and stochastic volatility. Some numerical results will be presented and discussed using finite element and Monte Carlo methods, for a bidimensional case.

Keywords


Levy processes, stochastic volatility, variational formulation, finite element method, Euler scheme, Monte Carlo method.

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