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Variance-Optimal Hedging for Time-Changed Levy Processes

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  • Jan Kallsen
  • Arnd Pauwels
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    Abstract

    In this article, we solve the variance-optimal hedging problem in stochastic volatility (SV) models based on time-changed Levy processes, that is, in the setup of Carr et al. (2003). The solution is derived using results for general affine models in the companion article [Kallsen and Pauwels (2009)].

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003669164
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 18 (2011)
    Issue (Month): 1 ()
    Pages: 1-28

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    Handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:1-28

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    Related research

    Keywords: Variance-optimal hedging; Stochastic volatility; Time-changed Levy process; Laplace transform;

    References

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    1. Ales Čern� & Jan Kallsen, 2008. "Mean-Variance Hedging And Optimal Investment In Heston'S Model With Correlation," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 473-492.
    2. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    3. Friedrich Hubalek & Carlo Sgarra, 2007. "Quadratic Hedging For The Bates Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 873-885.
    4. Jan Kallsen & Richard Vierthauer, 2009. "Quadratic hedging in affine stochastic volatility models," Review of Derivatives Research, Springer, vol. 12(1), pages 3-27, April.
    5. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
    6. Flavio Angelini & Stefano Herzel, 2007. "Measuring the error of dynamic hedging: a Laplace transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 33/2007, Università di Perugia, Dipartimento Economia, Finanza e Statistica.
    7. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
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    Cited by:
    1. Di Nunno, Giulia & Sjursen, Steffen, 2014. "BSDEs driven by time-changed Lévy noises and optimal control," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1679-1709.
    2. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.

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