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Local volatility in the Heston model: a Malliavin calculus approach

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  • Christian-Oliver Ewald

Abstract

We implement the Heston stochastic volatility model by using multidimensional Ornstein-Uhlenbeck processes and a special Girsanov transformation, and consider the Malliavin calculus of this model. We derive explicit formulas for the Malliavin derivatives of the Heston volatility and the log-price, and give a formula for the local volatility which is approachable by Monte-Carlo methods.

Suggested Citation

  • Christian-Oliver Ewald, 2005. "Local volatility in the Heston model: a Malliavin calculus approach," International Journal of Stochastic Analysis, Hindawi, vol. 2005, pages 1-16, January.
    • Handle: RePEc:hin:jnijsa:951429
    DOI: 10.1155/JAMSA.2005.307
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    Cited by:

    1. Koike, Takaaki & Saporito, Yuri & Targino, Rodrigo, 2022. "Avoiding zero probability events when computing Value at Risk contributions," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 173-192.
    2. 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.

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