A fast numerical method to price American options under the Bates model

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 price of an American option can be obtained as the solution of a linear complementarity problem governed by a partial integro-differential equation. In this paper, a numerical method for solving such a problem is proposed. In particular, first of all, using a Bermudan approximation and a Richardson extrapolation technique, the linear complementarity problem is reduced to a set of standard linear partial differential problems (see, for example, Ballestra and Sgarra, 2010; Chang et al. 2007, 2012). Then, these problems are solved using an ad hoc pseudospectral method which efficiently combines the Chebyshev polynomial approximation, an implicit/explicit time stepping and an operator splitting technique. Numerical experiments are presented showing that the novel algorithm is very accurate and fast and significantly outperforms other methods that have recently been proposed for pricing American options under the Bates model.