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

Abstract

This paper provides an efficient pricing method for forward starting options based on Shannon wavelet expansions. Specifically, we derive the pricing results under a more realistic stock model that incorporates the double exponential jump, stochastic jump intensity, and two-factor stochastic volatilities to capture various features observed in financial markets. We obtain the characteristic function related to the payoff function; then, the options can be well evaluated by the Shannon wavelet method. Numerical experiments show that this method is fast and accurate compared to the Monte Carlo simulation. Finally, we study the influences of changing some important parameters to further illustrate the robustness and stability of the model.