More Formulas for Implied Volatility

  • Archil Gulisashvili
Part of the Springer Finance book series (FINANCE)


The model-free asymptotic formulas for the implied volatility established in Chap.  9 are rather universal. It is shown in Chap. 10 that these formulas imply several known results, e.g., R. Lee’s moment formulas and the tail-wing formulas due to S. Benaim and P. Friz. Various new results can also be obtained from the model-free formulas, for example, sharp asymptotic formulas for the implied volatility in the Hull-White model, the Stein-Stein model, the Heston model, and in some stochastic volatility models with jumps. Chapter 10 also treats the “volatility smile”. This expression was coined to describe an observed feature of at-the-money options to have a smaller implied volatility than in-the-money or out-of-the-money options. The contents of Chap. 10 include a result of E. Renault and N. Touzi concerning the existence of volatility smile in uncorrelated stochastic volatility models. The chapter also discusses the SVI parameterization of the implied variance introduced by J. Gatheral.


Stock Price Asset Price Implied Volatility Price Process Asset Price Model 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Archil Gulisashvili
    • 1
  1. 1.Department of MathematicsOhio UniversityAthensUSA

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