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Asymptotic Equivalence In Lee'S Moment Formulas For The Implied Volatility, Asset Price Models Without Moment Explosions, And Piterbarg'S Conjecture

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  • ARCHIL GULISASHVILI

    (Department of Mathematics, Ohio University, Athens, Ohio 45701, USA)

Abstract

In this paper, we study the asymptotic behavior of the implied volatility in stochastic asset price models. We provide necessary and sufficient conditions for the validity of asymptotic equivalence in Lee's moment formulas, and obtain new asymptotic formulas for the implied volatility in asset price models without moment explosions. As an application, we prove a modified version of Piterbarg's conjecture. The asymptotic formula suggested by Piterbarg may be considered as a substitute for Lee's moment formula for the implied volatility at large strikes in the case of models without moment explosions. We also characterize the asymptotic behavior of the implied volatility in several special asset price models, e.g., the CEV model, the finite moment log-stable model of Carr and Wu, the Heston model perturbed by a compound Poisson process with double exponential law for jump sizes, and SV1 and SV2 models of Rogers and Veraart.

Suggested Citation

  • Archil Gulisashvili, 2012. "Asymptotic Equivalence In Lee'S Moment Formulas For The Implied Volatility, Asset Price Models Without Moment Explosions, And Piterbarg'S Conjecture," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-34.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:03:n:s0219024912500203
    DOI: 10.1142/S0219024912500203
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
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