How to make Dupire's local volatility work with jumps

Peter K. Friz; Stefan Gerhold; Marc Yor

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arXiv · 1302.5548

How to make Dupire's local volatility work with jumps

Peter K. Friz·Stefan Gerhold·Marc Yor

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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.

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Peter K. Friz, Stefan Gerhold, Marc Yor. 2013-02-22. How to make Dupire's local volatility work with jumps. https://arxiv.org/abs/1302.5548

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