FROM THE IMPLIED VOLATILITY SKEW TO A ROBUST CORRECTION TO BLACK-SCHOLES AMERICAN OPTION PRICES

Jean-Pierre Fouque (), George Papanicolaou () and K. Ronnie Sircar ()
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Jean-Pierre Fouque: Department of Mathematics, North Carolina State University, Raleigh NC 27695-8205, USA
George Papanicolaou: Department of Mathematics, Stanford University, Stanford CA 94305, USA
K. Ronnie Sircar: ORFE Department, Princeton University, Princeton, NJ 08544, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 04, 651-675

Abstract: We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of afixedboundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

Keywords: Black-Scholes model; American put options; stochastic volatility model; mean-reversion (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219024901001139

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