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Esscher transforms and the minimal entropy martingale measure for exponential Levy models

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  • Friedrich Hubalek
  • Carlo Sgarra
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    Abstract

    In this paper we offer a systematic survey and comparison of the Esscher martingale transform for linear processes, the Esscher martingale transform for exponential processes, and the minimal entropy martingale measure for exponential Levy models, and present some new results in order to give a complete characterization of those classes of measures. We illustrate the results with several concrete examples in detail.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680600573099
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    Bibliographic Info

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

    Volume (Year): 6 (2006)
    Issue (Month): 2 ()
    Pages: 125-145

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    Handle: RePEc:taf:quantf:v:6:y:2006:i:2:p:125-145

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    Related research

    Keywords: Esscher transform; Minimal entropy; Martingale measures; Levy processes;

    References

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    1. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
    2. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
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    Cited by:
    1. Matthias Fengler & Helmut Herwartz & Christian Werner, 2010. "A dynamic copula approach to recovering the index implied volatility skew," University of St. Gallen Department of Economics working paper series 2010 1132, Department of Economics, University of St. Gallen, revised Nov 2011.
    2. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
    3. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    4. Thorsten Rheinl\"ander & Michael Schmutz, 2012. "Quasi self-dual exponential L\'evy processes," Papers 1201.5132, arXiv.org.

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