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An application of Malliavin Calculus to Finance

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  • Arturo Kohatsu-Higa
  • Miquel Montero

Abstract

In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available. The Greeks are computed through Monte Carlo simulation.

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  • Arturo Kohatsu-Higa & Miquel Montero, 2001. "An application of Malliavin Calculus to Finance," Papers cond-mat/0111563, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/0111563
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    File URL: http://arxiv.org/pdf/cond-mat/0111563
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    References listed on IDEAS

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    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
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