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A Class of Financial Products and Models Where Super-replication Prices are Explicit

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • L. Carassus

    (Laboratoire de Probabilités et Modèles Aléatoires - Université Paris 7 - Denis Diderot - Case 7012 - 2, place Jussieu - 75251 Paris cedex 05, France)

  • E. Gobet

    (Laboratoire Jean Kuntzman - ENSIMAG INP Grenoble - BP 53 - 38041 Grenoble cedex 09, France)

  • E. Temam

    (Laboratoire de Probabilités et Modèles Aléatoires - Université Paris 7 - Denis Diderot - Case 7012 - 2, place Jussieu - 75251 Paris cedex 05, France)

Abstract

We consider a multidimensional financial model with mild conditions on the underlying asset price process. The trading is only allowed at some fixed discrete times and the strategy is constrained to lie in a closed convex cone. We show how the minimal cost of a super hedging strategy can be easily computed by a backward recursive scheme. As an application, when the underlying asset follows a stochastic differential equation including stochastic volatility or Poisson jumps, we compute those super-replication prices for a range of European and American style options, including Asian, Lookback or Barrier Options. We also perform some multidimensional computations.

Suggested Citation

  • L. Carassus & E. Gobet & E. Temam, 2007. "A Class of Financial Products and Models Where Super-replication Prices are Explicit," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 4, pages 67-84, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0004
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    Citations

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    Cited by:

    1. Francesca Biagini & Lukas Gonon & Thomas Reitsam, 2023. "Neural network approximation for superhedging prices," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 146-184, January.
    2. Nabil Kahalé, 2017. "Superreplication of Financial Derivatives via Convex Programming," Management Science, INFORMS, vol. 63(7), pages 2323-2339, July.
    3. Francesca Biagini & Lukas Gonon & Thomas Reitsam, 2021. "Neural network approximation for superhedging prices," Papers 2107.14113, arXiv.org.

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