How to make Dupire's local volatility work with jumps
Pricing of Securities
2013-02-25 v1
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.
Cite
@article{arxiv.1302.5548,
title = {How to make Dupire's local volatility work with jumps},
author = {Peter K. Friz and Stefan Gerhold and Marc Yor},
journal= {arXiv preprint arXiv:1302.5548},
year = {2013}
}