CRIF Working Paper No. 02008

Finite Moment Log Stable Process and Option Pricing

Title: Finite Moment Log Stable Process and Option Pricing

Authors: Peter Carr (New York University)

              Liuren Wu (Fordham University)

Contact: wu@fordham.edu

Keywords: Volatility smirk, central limit theorem, Levy α-stable motion, self-similarity, option pricing.

JEL Classification: G12, G13, F31, C14

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.  

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Comments: The paper is forthcoming in Journal of Finance.