The Finite Moment Log Stable Process and Option Pricing

Posted: 20 Sep 2003

See all articles by Liuren Wu

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Peter Carr

New York University Finance and Risk Engineering

Abstract

We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.

Suggested Citation

Wu, Liuren and Carr, Peter P., The Finite Moment Log Stable Process and Option Pricing. Journal of Finance, Vol. 58, pp. 753-778, April 2003. Available at SSRN: https://ssrn.com/abstract=416663

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

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

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