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Error Calculus and Path Sensitivity in Financial Models

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  • Nicolas Bouleau

Abstract

In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus that is an extension of the Malliavin calculus based on Dirichlet forms. Although useful also in physics, this error calculus is well adapted to stochastic analysis and seems to be the best practicable in finance. This tool is explained here intuitively and with some simple examples.

Suggested Citation

  • Nicolas Bouleau, 2003. "Error Calculus and Path Sensitivity in Financial Models," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 115-134, January.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:115-134
    DOI: 10.1111/1467-9965.00009
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    References listed on IDEAS

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    1. 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.
    2. Bouleau, Nicolas & Lamberton, Damien, 1989. "Residual risks and hedging strategies in Markovian markets," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 131-150, October.
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    Cited by:

    1. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Maria Elvira Mancino & Simona Sanfelici, 2020. "Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks," Risks, MDPI, vol. 8(4), pages 1-17, November.
    3. Luca Regis & Simone Scotti, 2008. "Risk Premium Impact in the Perturbative Black Scholes Model," Papers 0806.0307, arXiv.org.
    4. Nicolas Bouleau & Christophe Chorro, 2004. "Error structures and parameter estimation," Cahiers de la Maison des Sciences Economiques b04079, Université Panthéon-Sorbonne (Paris 1).
    5. Christophe Chorro, 2004. "On an extension of the Hilbertian central limit theorem to Dirichlet forms," Cahiers de la Maison des Sciences Economiques b04080, Université Panthéon-Sorbonne (Paris 1).

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