A Note on Relative Efficiency of Some Numerical Methods for Pricing of American Options Under Levy Processes

40 Pages Posted: 28 Oct 2004

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

Date Written: October 11, 2004

Abstract

We analyze properties of prices of American options under Levy processes, and the related difficulties for design of accurate and efficient numerical methods for pricing of American options. The case of Levy processes with insignificant diffusion component and jump part of infinite activity but finite variation (the case most relevant to practice according to the empirical study in Carr et. al., Journ. of Business (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 time to expiry is large, but two methods: 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 2 months or more, and the relative error 1-2% 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, IJTAF (2004), is the best choice.

Keywords: American options, Levy processes, numerical methods

Suggested Citation

Levendorskii, Sergei Z. and Kudryavtsev, Oleg E. and Zherder, Vadim M., A Note on Relative Efficiency of Some Numerical Methods for Pricing of American Options Under Levy Processes (October 11, 2004). Available at SSRN: https://ssrn.com/abstract=610542 or http://dx.doi.org/10.2139/ssrn.610542

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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