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The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models

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  • Thorsten Rheinlander
  • Gallus Steiger

Abstract

We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have treated either the geometric L\'{e}vy case or continuous price processes with an orthogonal volatility process. We proceed by linking the entropy measure to a certain semi-linear integro-PDE for which we prove the existence of a classical solution.

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  • Thorsten Rheinlander & Gallus Steiger, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," Papers math/0610219, arXiv.org.
    • Handle: RePEc:arx:papers:math/0610219
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    References listed on IDEAS

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    1. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466, October.
    2. Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
    3. Tahir Choulli & Christophe Stricker, 2005. "Minimal Entropy–Hellinger Martingale Measure In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 465-490, July.
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    Cited by:

    1. Markus Hess, 2019. "Optimal Equivalent Probability Measures under Enlarged Filtrations," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 813-839, December.
    2. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062.
    3. 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.
    4. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    5. Jan Kallsen & Johannes Muhle-Karbe, 2009. "Utility maximization in models with conditionally independent increments," Papers 0911.3608, arXiv.org.
    6. 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.

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