Stepping Through Fourier Space

RISK, pp. 78-83, July 2009

8 Pages Posted: 14 Oct 2008 Last revised: 29 Jun 2011

See all articles by Sebastian Jaimungal

Sebastian Jaimungal

University of Toronto - Department of Statistics

Vladimir Surkov

RBC Capital Markets

Date Written: October 9, 2008

Abstract

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.

Keywords: Option pricing, Levy processes, regime switching, Fourier methods, American options, catastrophe options

JEL Classification: G12, G13

Suggested Citation

Jaimungal, Sebastian and Surkov, Vladimir, Stepping Through Fourier Space (October 9, 2008). RISK, pp. 78-83, July 2009. Available at SSRN: https://ssrn.com/abstract=1281743

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

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

HOME PAGE: http://www.utstat.utoronto.ca/sjaimung

Vladimir Surkov (Contact Author)

RBC Capital Markets ( email )

New York, NY
United States

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