How to Make Dupire's Local Volatility Work with Jumps

7 Pages Posted: 28 Feb 2013

See all articles by Peter Friz

Peter Friz

Technische Universität Berlin (TU Berlin)

Stefan Gerhold

Vienna University of Technology

Marc Yor

Universite Paris

Date Written: February 22, 2013

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.

Keywords: Local volatility, Fokker-Planck equation, Levy processes

JEL Classification: G13

Suggested Citation

Friz, Peter and Gerhold, Stefan and Yor, Marc, How to Make Dupire's Local Volatility Work with Jumps (February 22, 2013). Available at SSRN: https://ssrn.com/abstract=2224876 or http://dx.doi.org/10.2139/ssrn.2224876

Peter Friz

Technische Universität Berlin (TU Berlin) ( email )

Straße des 17
Juni 135
Berlin, 10623
Germany

Stefan Gerhold (Contact Author)

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

Marc Yor

Universite Paris ( email )

223 Rue Saint-Honore
Paris, 75775
France

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