Fourier Space Time-Stepping for Option Pricing With Levy Models
30 Pages Posted: 10 Oct 2007 Last revised: 1 Jul 2009
Date Written: March 14, 2007
Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in the classical Black-Scholes-Merton model. Unfortunately, the resulting pricing problem requires solving a more difficult partial-integro differential equation (PIDE) and although several approaches for solving the PIDE have been suggested in the literature, none are entirely satisfactory. All treat the integral and diffusive terms asymmetrically and are difficult to extend to higher dimensions. We present a new, efficient algorithm, based on transform methods, which symmetrically treats the diffusive and integrals terms, is applicable to a wide class of path-dependent options (such as Bermudan, barrier, and shout options) and options on multiple assets, and naturally extends to regime-switching Levy models.
Keywords: Fourier space time-stepping, option pricing, Levy processes, multi-asset options
JEL Classification: G12, G13, C61, C63
Suggested Citation: Suggested Citation
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