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Pricing American Options Fitting the Smile

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  • M. A. H. Dempster
  • D. G. Richards
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    Abstract

    This paper is a compendium of results-theoretical and computational-from a series of recent papers developing a new American option valuation technique based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given, as is the analysis needed to solve the inverse problem of determining local (one-factor) volatility from market data. The ideas behind a fast accurate revised simplex method, whose performance is linear in time and space discretizations, are described and the practicalities of fitting the volatility smile are discussed. Numerical results are presented which show the LP valuation technique to be extremely fast-lattice speed with PDE accuracy. American options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile. Copyright Blackwell Publishers, Inc..

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 10 (2000)
    Issue (Month): 2 ()
    Pages: 157-177

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    Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:157-177

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    Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627

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    Cited by:
    1. Matthias R. Fengler, 2005. "Arbitrage-Free Smoothing of the Implied Volatility Surface," SFB 649 Discussion Papers SFB649DP2005-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    3. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
    4. Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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