The Finite Moment Log Stable Process and Option Pricing

Peter Carr and Liuren Wu ()
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Peter Carr: New York University

Finance from EconWPA

Abstract: We document a surprising pattern in market prices of S&P 500 index options. 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.

Keywords: Volatility smirk; central limit theorem; Levy a­lpha-stable motion; self­similarity; option pricing. (search for similar items in EconPapers)
JEL-codes: G12 G13 F31 C14 (search for similar items in EconPapers)
Date: 2002-08-30
Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 42 ; figures: included. produced via dvipdfm
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Journal Article: The Finite Moment Log Stable Process and Option Pricing (2003)
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0207012

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