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Regular Variation And Smile Asymptotics

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  • S. Benaim
  • P. Friz

Abstract

We consider risk‐neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.

Suggested Citation

  • S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12, January.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:1:p:1-12
    DOI: 10.1111/j.1467-9965.2008.00354.x
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    References listed on IDEAS

    as
    1. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    2. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
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