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Forward equations for option prices in semimartingale models

Author

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  • Amel Bentata

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Rama Cont

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

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 and allows to retrieve various forward equations previously obtained for option prices in a unified framework.

Suggested Citation

  • Amel Bentata & Rama Cont, 2009. "Forward equations for option prices in semimartingale models," Working Papers hal-00445641, HAL.
    • Handle: RePEc:hal:wpaper:hal-00445641
    Note: View the original document on HAL open archive server: https://hal.science/hal-00445641v3
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    Cited by:

    1. Amel Bentata & Rama Cont, 2012. "Short-time asymptotics for marginal distributions of semimartingales," Papers 1202.1302, arXiv.org.
    2. Rama Cont & Nicolas Lantos & Olivier Pironneau, 2011. "A reduced basis for option pricing," Post-Print hal-00522410, HAL.
    3. Forde, Martin, 2014. "On the Markovian projection in the Brunick–Shreve mimicking result," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 98-105.
    4. Amel Bentata & Rama Cont, 2012. "Short-time asymptotics for marginal distributions of semimartingales," Working Papers hal-00667112, HAL.

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