FFT-network for bivariate Lévy option pricing

We propose a two-dimensional fast Fourier transform (FFT) network to retrieve the prices of options that depend on two Lévy processes. Applications include, but are not limited to, the valuation of options on two stocks under the Lévy processes, and options on a single stock under a random time-change Lévy process. The proposed numerical scheme can be applied to different multivariate Lévy 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 Lévy processes. Such a model is also called the random time-changed Lévy process. Numerical examples are given to demonstrate the efficiency and accuracy of FFT-network applied to exotic and American-style options.