How to make Dupire's local volatility work with jumps
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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- Yor, Marc & Madan, Dilip B. & Carr, Peter & Geman, Hélyette, 2004. "From Local Volatility to Local Levy Models," Economics Papers from University Paris Dauphine 123456789/1448, Paris Dauphine University.
- Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, 07.
- Peter Carr & Helyette Geman & Dilip Madan & Marc Yor, 2004. "From local volatility to local Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 581-588.
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