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Finance and Stochastics

, Volume 19, Issue 3, pp 617–651 | Cite as

Forward equations for option prices in semimartingale models

Article

Abstract

We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a—possibly discontinuous—semimartingale. This result generalizes Dupire’s forward equation to a large class of non-Markovian models with jumps.

Keywords

Forward equation Dupire equations Jump process Semimartingale Tanaka–Meyer formula Markovian projection Call option Option pricing 

Mathematics Subject Classification

60H30 91G20 35S10 91G80 

JEL Classification

C60 G13 

Notes

Acknowledgements

We thank Damien Lamberton for numerous remarks, which helped improve the manuscript. Substantial assistance from an Associate Editor and the Editor is also gratefully acknowledged. Any remaining errors are our own.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresCNRS—Université de Paris VIParisFrance

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