Self-Decomposability and Option Pricing

27 Pages Posted: 13 Dec 2006

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Hélyette Geman

University of London - Economics, Mathematics and Statistics

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Marc Yor

Universite Paris

Abstract

The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and maturities at a point of time. Considerations of parameter stability over time suggest a preference for two of these models. Currently, there are several option pricing models with 6-10 free parameters that deliver a comparable level of performance in synthesizing option prices. The dimension reduction attained here should prove useful in studying the variation over time of option prices.

Suggested Citation

Carr, Peter P. and Geman, Helyette and Madan, Dilip B. and Yor, Marc, Self-Decomposability and Option Pricing. Mathematical Finance, Vol. 17, No. 1, pp. 31-57, January 2007. Available at SSRN: https://ssrn.com/abstract=951330 or http://dx.doi.org/10.1111/j.1467-9965.2007.00293.x

Peter P. Carr (Contact Author)

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Helyette Geman

University of London - Economics, Mathematics and Statistics ( email )

Malet Street
London, WC1E 7HX
United Kingdom

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Marc Yor

Universite Paris ( email )

223 Rue Saint-Honore
Paris, 75775
France

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