Fast and Accurate Pricing of Barrier Options Under Levy Processes

32 Pages Posted: 6 Dec 2007

See all articles by Oleg E. Kudryavtsev

Oleg E. Kudryavtsev

Russian Customs Academy Rostov Branch - Department of Informatics

Sergei Levendorskii

Calico Science Consulting

Date Written: November 30, 2007

Abstract

We suggest two new fast and accurate methods, Fast Wiener-Hopf method (WHF-method) and Iterative Wiener-Hopf method (IWH-method), for pricing barrier options for a wide class of L'evy processes. Both methods use the Wiener-Hopf factorization and Fast Fourier Transform algorithm. Using an accurate albeit relatively slow finite-difference algorithm developed in Levendorski et al. (2006) (FDS-method), we demonstrate accuracy and fast convergence of these methods for processes of finite variation. We explain that the convergence of the methods must be better for processes of infinite variation, and, as a certain supporting evidence, demonstrate with numerical examples that the results obtained by the two methods are in extremely good agreement. Finally, we use FDS, WHF and IWH-methods to demonstrate that Cont and Volchkova method (CV-method), which is based on the approximation of small jumps by an additional diffusion, may lead to sizable relative errors, especially near the barrier and strike. The reason is that CV-method presumes that the option price is of twice continuously differentiable up to the barrier, whereas for processes without Gaussian component, it is typically not smooth at the barrier.

Keywords: barrier options, Levy processes, numerical methods

JEL Classification: D81, C61, G31

Suggested Citation

Kudryavtsev, Oleg E. and Levendorskii, Sergei Z., Fast and Accurate Pricing of Barrier Options Under Levy Processes (November 30, 2007). Available at SSRN: https://ssrn.com/abstract=1040061 or http://dx.doi.org/10.2139/ssrn.1040061

Oleg E. Kudryavtsev

Russian Customs Academy Rostov Branch - Department of Informatics ( email )

Budennovskiy 20
Rostov-on-Don, 344011
Russia

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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