Codice QDD 42 Titolo The Evaluation of American Options in a Stochastic Volatility Model with Jumps: a Finite Element Approach Data 2009-04-06 Autore/i Ballestra, L.V.; Sgarra, C. Link Download full text Abstract In the present paper we consider the problem of pricing American options in the framework of a well-known stochastic volatility model with jumps, the Bates model. According to this model the asset price is assumed to follow a jump-diffusion equation in which the jump term consists of a Lévy process of compound Poisson type, while the volatility is modeled as a CIR-type process correlated with the asset price. In this model the American option valuation is reduced to a final-free-boundary-value partial integro-differential problem. Using a Richardson extrapolation technique this problem is reduced to a partial integro-differential problems with fixed boundary. Then the transformed problem is solved using an ad-hoc finite element method which efficiently combines an operator splitting technique with a non-uniform mesh of right-angled triangles. Numerical experiments are presented showing that the option pricing algorithm developed in this paper is very accurate and fast.