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How to make Dupire's local volatility work with jumps

Peter K. Friz, Stefan Gerhold and Marc Yor

Quantitative Finance, 2013, vol. 14, issue 8, 1327-1331

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.

Date: 2013
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Handle: RePEc:taf:quantf:v:14:y:2013:i:8:p:1327-1331