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.

A Shannon Wavelet Method for Pricing Forward Starting Options under the Double Exponential Jump Framework with Two-Factor Stochastic Volatilities

“…For Monte Carlo method, we use 100,000 numbers of simulations with 200 numbers of time steps. e COS method has been proved to be highly e cient and accurate in a wealth of literature [17,19,22,28]. Monte Carlo simulation is a typical numerical method in the domain of option pricing, and it can be exibly used for various exotic options and thus becomes one of the most common approaches in practice.…”