Fourier Space Time-Stepping for Option Pricing With Levy Models

30 Pages Posted: 10 Oct 2007 Last revised: 1 Jul 2009

See all articles by Kenneth R. Jackson

Kenneth R. Jackson

University of Toronto - Department of Computer Science

Sebastian Jaimungal

University of Toronto - Department of Statistics

Vladimir Surkov

RBC Capital Markets

Date Written: March 14, 2007

Abstract

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

Jackson, Kenneth R. and Jaimungal, Sebastian and Surkov, Vladimir, Fourier Space Time-Stepping for Option Pricing With Levy Models (March 14, 2007). Journal of Computational Finance, Vol. 12, No. 2, pp. 1-29, 2008. Available at SSRN: https://ssrn.com/abstract=1020209 or http://dx.doi.org/10.2139/ssrn.1020209

Kenneth R. Jackson

University of Toronto - Department of Computer Science ( email )

Sandford Fleming Building
10 King's College Road, Room 3302
Toronto, Ontario M5S 3G4
Canada

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Vladimir Surkov (Contact Author)

RBC Capital Markets ( email )

New York, NY
United States

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