Stepping Through Fourier Space

Diverse finite-difference schemes for solving pricing problems with Levy underliers have been used in the literature. Invariably, the integral and diffusive terms are treated asymmetrically, large jumps are truncated, the methods are difficult to extend to higher dimensions and cannot easily incorporate regime switching or stochastic volatility. We present a new efficient approach which switches between Fourier and real space as time propagates backwards. We dub this method Fourier Space Time-Stepping (FST). The FST method applies to regime switching Levy models and is applicable to a wide class of path-dependent options (such as Bermudan, barrier, shout and catastrophe linked options) and options on multiple assets