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The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps

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  • Fred Benth

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  • Thilo Meyer-Brandis

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Abstract

We derive the density process of the minimal entropy martingale measure in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard [2]. The density is represented by the logarithm of the value function for an investor with exponential utility and no claim issued, and a Feynman-Kac representation of this function is provided. The dynamics of the processes determining the price and volatility are explicitly given under the minimal entropy martingale measure, and we derive a Black & Scholes equation with integral term for the price dynamics of derivatives. It turns out that the minimal entropy price of a derivative is given by the solution of a coupled system of two integro-partial differential equations. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Fred Benth & Thilo Meyer-Brandis, 2005. "The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps," Finance and Stochastics, Springer, vol. 9(4), pages 563-575, October.
  • Handle: RePEc:spr:finsto:v:9:y:2005:i:4:p:563-575
    DOI: 10.1007/s00780-005-0161-z
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    Citations

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    Cited by:

    1. Smimou, K. & Bector, C.R. & Jacoby, G., 2007. "A subjective assessment of approximate probabilities with a portfolio application," Research in International Business and Finance, Elsevier, vol. 21(2), pages 134-160, June.
    2. Choulli, Tahir & Vandaele, Nele & Vanmaele, Michèle, 2010. "The Föllmer-Schweizer decomposition: Comparison and description," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 853-872, June.
    3. Rheinlander, Thorsten & Steiger, Gallus, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," LSE Research Online Documents on Economics 16351, London School of Economics and Political Science, LSE Library.
    4. Dirk Becherer, 2007. "Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging," Papers math/0702405, arXiv.org.
    5. Hubalek, Friedrich & Sgarra, Carlo, 2009. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2137-2157, July.
    6. Wanyang Dai, 2014. "Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processes," Papers 1410.0991, arXiv.org, revised Aug 2015.

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