How to make Dupire's local volatility work with jumps
AbstractThere 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.5548.
Date of creation: Feb 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-02 (All new papers)
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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.
- repec:ner:dauphi:urn:hdl:123456789/1448 is not listed on IDEAS
- Peter Carr & Helyette Geman & Dilip Madan & Marc Yor, 2004. "From local volatility to local Levy models," Quantitative Finance, Taylor and Francis Journals, vol. 4(5), pages 581-588.
- Cont, Rama & Voltchkova, Ekaterina, 2005.
"Integro-Differential Equations for Option Prices in Exponential Lévy Models,"
Open Access publications from University of Toulouse 1 Capitole
http://neeo.univ-tlse1.fr, University of Toulouse 1 Capitole.
- 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.
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