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A note on essential smoothness in the Heston model

Author

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  • Martin Forde
  • Antoine Jacquier
  • Aleksandar Mijatović

Abstract

This note studies an issue relating to essential smoothness that can arise when the theory of large deviations is applied to a certain option pricing formula in the Heston model. The note identifies a gap, based on this issue, in the proof of Corollary 2.4 in \cite{FordeJacquier10} and describes how to circumvent it. This completes the proof of Corollary 2.4 in \cite{FordeJacquier10} and hence of the main result in \cite{FordeJacquier10}, which describes the limiting behaviour of the implied volatility smile in the Heston model far from maturity.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Martin Forde & Antoine Jacquier & Aleksandar Mijatović, 2011. "A note on essential smoothness in the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 781-784, December.
    • Handle: RePEc:spr:finsto:v:15:y:2011:i:4:p:781-784
    DOI: 10.1007/s00780-011-0162-z
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    Cited by:

    1. Martin Forde & Stefan Gerhold & Benjamin Smith, 2021. "Small‐time, large‐time, and H→0 asymptotics for the Rough Heston model," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 203-241, January.

    More about this item

    Keywords

    Essential smoothness; Large deviation principle; Heston model; 60G44; 91B70; 91B25; C02; C63; G12; G13;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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