How to make Dupire's local volatility work with jumps
Peter K. Friz,
Stefan Gerhold and
Quantitative Finance, 2013, vol. 14, issue 8, 1327-1331
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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