An efficient pricing algorithm for American options with double stochastic volatilities and double jumps

Abstract

The purpose of the paper is to provide an efficient pricing algorithm for American options with stochastic volatilities and jumps. This paper extends the double Heston model with double exponential jumps and derives the characteristic function of the model by Feynman–Kac theorem. With the obtained characteristic function, this paper also extends the Fourier-cosine expansion method for pricing Bermudan options to the model. Based on the COS method, this paper approximates American options by using Richardson extrapolation schemes on a series of Bermudan options and provides a pricing algorithm for American put options. Numerical results show that the proposed pricing algorithm is efficient, especially for short-term American put options.