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Option pricing in bilateral Gamma stock models

Author

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  • Küchler Uwe
  • Tappe Stefan

    (ETH Zürich, Department of Mathematics, Zürich, Schweiz)

Abstract

In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, p-optimal martingale measures, bilateral Esscher transforms and the minimal martingale measure. We illustrate our theory by a numerical example.

Suggested Citation

  • Küchler Uwe & Tappe Stefan, 2009. "Option pricing in bilateral Gamma stock models," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 281-307, December.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:4:p:281-307:n:4
    DOI: 10.1524/stnd.2009.1048
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    References listed on IDEAS

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    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    2. Küchler, Uwe & Tappe, Stefan, 2008. "On the shapes of bilateral Gamma densities," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2478-2484, October.
    3. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556, October.
    4. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    5. Jan Kallsen, 2000. "Optimal portfolios for exponential Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 357-374, August.
    6. Aleš Černý & Jan Kallsen, 2008. "A Counterexample Concerning The Variance‐Optimal Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 305-316, April.
    7. Christian Bender & Christina Niethammer, 2008. "On q-optimal martingale measures in exponential Lévy models," Finance and Stochastics, Springer, vol. 12(3), pages 381-410, July.
    8. 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.
    9. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    2. Edit Rroji & Lorenzo Mercuri, 2015. "Mixed tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1559-1569, September.
    3. Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, vol. 181(1), pages 53-63.

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