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How to make Dupire's local volatility work with jumps

Author

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  • Peter K. Friz
  • Stefan Gerhold
  • Marc Yor

Abstract

There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note, we attempt to explain why. In particular, we propose a regularization procedure of the option data so that Dupire's local vol diffusion process recreates the correct option prices, even in manifest presence of jumps.

Suggested Citation

  • Peter K. Friz & Stefan Gerhold & Marc Yor, 2013. "How to make Dupire's local volatility work with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1327-1331, December.
    • Handle: RePEc:taf:quantf:v:14:y:2013:i:8:p:1327-1331
    DOI: 10.1080/14697688.2013.874622
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    Cited by:

    1. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "Analytical expansions for parabolic equations," Papers 1312.3314, arXiv.org, revised Nov 2014.
    2. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2014. "Asymptotics for $d$-dimensional L\'evy-type processes," Papers 1404.3153, arXiv.org, revised Nov 2014.

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