FFT-network for bivariate Lévy option pricing

Abstract

We propose a two-dimensional fast Fourier transform (FFT) network to retrieve the prices of options that depend on two Levy processes. Applications include, but are not limited to, the valuation of options on two stocks under the Levy processes, and options on a single stock under a random time-change Levy process. The proposed numerical scheme can be applied to different multivariate Levy constructions such as subordination and linear combination provided that the joint characteristic function is available. The proposed FFT-network can be thought of as a lattice approach implemented through the characteristic function. With the prevalent implementation of FFT, the network approach results in significant computational time reduction while maintaining satisfactory accuracy. Furthermore, we investigate option pricing on a single asset where the asset return and its volatility are driven by a pair of dependent Levy processes. Such a model is also called the random time-changed Levy process. Numerical examples are given to demonstrate the efficiency and accuracy of FFT-network applied to exotic and American-style options.