The Relative Efficiency of Numerical Methods for Pricing American Options Under LéVy Processes

Posted: 10 May 2006

See all articles by Sergei Levendorskii

Sergei Levendorskii

Calico Science Consulting

Oleg E. Kudryavtsev

Russian Customs Academy Rostov Branch - Department of Informatics

Vadim M. Zherder

Rostov State Economic University; Russian Customs Academy Rostov Branch - Department of Informatics

Abstract

We analyze properties of prices of American options under Lévy processes and the related difficulties for design of accurate and efficient numerical methods for pricing of American options. The case of Lévy processes with an insignificant diffusion component and jump part of infinite activity but finite variation (the case most relevant in practice according to the empirical study in Carr et al (2002)) appears to be the most difficult. Several numerical methods suggested for this case are discussed and compared. It is shown that approximations by diffusions with embedded jumps may be too inaccurate unless the time to expiry is large. However, the fitting by a diffusion with embedded exponentially distributed jumps and a new finite difference scheme suggested in the paper can be used as good complements, which ensure accurate and fast calculation of the option prices both close to expiry and far from it.We demonstrate that if the time to expiry is two months or more, and the relative error 2-3% is admissible, then the fitting by a diffusion with embedded exponentially distributed jumps and the calculation of prices using the semi-explicit pricing procedure in Levendorskii (2004a) is the best choice.

Keywords: American options, Lévy processes, Lévy, Carr et al (2002), LevendorskiˇI (2004a)

Suggested Citation

Levendorskii, Sergei Z. and Kudryavtsev, Oleg E. and Zherder, Vadim M., The Relative Efficiency of Numerical Methods for Pricing American Options Under LéVy Processes. Journal of Computational Finance, Vol. 9, No. 2, Spring 2006. Available at SSRN: https://ssrn.com/abstract=900321

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

Oleg E. Kudryavtsev

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

Budennovskiy 20
Rostov-on-Don, 344011
Russia

Vadim M. Zherder

Rostov State Economic University

Bolshaya Sadovaya str., 62
Rostov-on-Don, 344007
Russia

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

Budennovskiy 20
Rostov-on-Don, 344011
Russia

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