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

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  • 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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    12. Uwe Kuchler & Stefan Tappe, 2019. "Option pricing in bilateral Gamma stock models," Papers 1907.09862, arXiv.org.
    13. Khaled Salhi, 2017. "Pricing European options and risk measurement under exponential Lévy models — a practical guide," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-36, June.
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    15. 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.
    16. George Bouzianis & Lane P. Hughston, 2019. "Determination Of The Lévy Exponent In Asset Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-18, February.
    17. Constantinos Kardaras, 2008. "No-Free-Lunch equivalences for exponential Levy models," Papers 0803.2169, arXiv.org.
    18. Michail Anthropelos & Michael Kupper & Antonis Papapantoleon, 2018. "An Equilibrium Model for Spot and Forward Prices of Commodities," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 152-180, February.
    19. 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.
    20. Uwe Kuchler & Stefan Tappe, 2019. "Exponential stock models driven by tempered stable processes," Papers 1907.05142, arXiv.org.
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    22. 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.
    23. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, August.
    24. 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.
    25. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.

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