Approximating Levy Processes with a View to Option Pricing

22 Pages Posted: 14 May 2009

See all articles by John Crosby

John Crosby

affiliation not provided to SSRN

Nolwenn Le Saux

affiliation not provided to SSRN

Aleksandar Mijatovic

Imperial College London

Date Written: May 13, 2009

Abstract

We examine how to approximate a Levy process by a hyperexponential jump-diffusion (HEJD) process, composed of Brownian motion and of an arbitrary number of sums of compound Poisson processes with double exponentially distributed jumps. This approximation will facilitate the pricing of exotic options since HEJD processes have a degree of tractability that other Levy processes do not have. The idea behind this approximation has been applied to option pricing by [Asmussen et al. 2007] and [Jeannin & Pistorius 2008]. In this paper we introduce a more systematic methodology for constructing this approximation which allow us to compute the intensity rates, the mean jump sizes and the volatility of the approximating HEJD process (almost) analytically. Our methodology is very easy to implement. We compute vanilla option prices and barrier option prices using the approximating HEJD process and we compare our results to those obtained from other methodologies in the literature. We demonstrate that our methodology gives very accurate option prices and that these prices are more accurate than those obtained from existing methodologies for approximating Levy processes by HEJD processes.

Keywords: Levy process, stochastic approximation, barrier and vanilla pricing

Suggested Citation

Crosby, John and Le Saux, Nolwenn and Mijatovic, Aleksandar, Approximating Levy Processes with a View to Option Pricing (May 13, 2009). Available at SSRN: https://ssrn.com/abstract=1403919 or http://dx.doi.org/10.2139/ssrn.1403919

John Crosby

affiliation not provided to SSRN ( email )

Nolwenn Le Saux

affiliation not provided to SSRN ( email )

Aleksandar Mijatovic (Contact Author)

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/a.mijatovic

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