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Refined wing asymptotics for the Merton and Kou jump diffusion models

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  • Stefan Gerhold
  • Johannes F. Morgenbesser
  • Axel Zrunek

Abstract

Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features an interesting "almost power law" tail.

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  • Stefan Gerhold & Johannes F. Morgenbesser & Axel Zrunek, 2014. "Refined wing asymptotics for the Merton and Kou jump diffusion models," Papers 1401.1954, arXiv.org.
    • Handle: RePEc:arx:papers:1401.1954
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    References listed on IDEAS

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    1. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    2. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12, January.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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