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

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Listed:
  • Friedrich Hubalek
  • Carlo Sgarra

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.

Suggested Citation

  • Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
  • Handle: RePEc:taf:quantf:v:6:y:2006:i:2:p:125-145
    DOI: 10.1080/14697680600573099
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    1. repec:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500165 is not listed on IDEAS
    2. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
    3. Michail Anthropelos & Michael Kupper & Antonis Papapantoleon, 2015. "An equilibrium model for spot and forward prices of commodities," Papers 1502.00674, arXiv.org, revised Jan 2017.
    4. 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.
    5. Laura Ballota & Griselda Deelstra & Grégory Rayée, 2015. "Quanto Implied Correlation in a Multi-Lévy Framework," Working Papers ECARES ECARES 2015-36, ULB -- Universite Libre de Bruxelles.
    6. Truong, Chi & Trück, Stefan, 2016. "It’s not now or never: Implications of investment timing and risk aversion on climate adaptation to extreme events," European Journal of Operational Research, Elsevier, vol. 253(3), pages 856-868.
    7. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
    8. S. Cawston & L. Vostrikova, 2010. "$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point," Papers 1004.3525, arXiv.org, revised Jun 2011.
    9. Küchler Uwe & Tappe Stefan, 2009. "Option pricing in bilateral Gamma stock models," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 281-307, December.
    10. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
    11. Constantinos Kardaras, 2009. "No-Free-Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187.
    12. Thorsten Rheinlander & Michael Schmutz, 2012. "Quasi self-dual exponential L\'evy processes," Papers 1201.5132, arXiv.org.
    13. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2015. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," School of Economics Working Papers 2015-17, University of Adelaide, School of Economics.
    14. Tsukasa Fujiwara, 2009. "The Minimal Entropy Martingale Measures for Exponential Additive Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 65-95, March.

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