The Finite Moment Log Stable Process and Option Pricing


  • Peter Carr,

  • Liuren Wu

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    • Carr is from the Courant Institute, New York University; Wu is from the Graduate School of Business, Fordham University. The authors thank Rick Green (the editor), an anonymous referee, Alexander David, Patrick Hagan, Takaki Hayashi, Andrew Matytsin, J. Huston McCulloch, Murad Taqqu, Eric Reiner, and participants of the 2001 WFA conference and the 2000 Columbia Mathematical Finance Seminar for helpful suggestions.


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.