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Exponential stock models driven by tempered stable processes

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  • Uwe Kuchler
  • Stefan Tappe

Abstract

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measures having minimal distance to the physical probability measure. Moreover, we provide pricing formulae for European call options and perform a case study.

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  • Uwe Kuchler & Stefan Tappe, 2019. "Exponential stock models driven by tempered stable processes," Papers 1907.05142, arXiv.org.
    • Handle: RePEc:arx:papers:1907.05142
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    1. Bianchi, Michele Leonardo & Rachev, Svetlozar T. & Kim, Young Shin & Fabozzi, Frank J., 2011. "Tempered infinitely divisible distributions and processes," Working Paper Series in Economics 26, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Svetlana I. Boyarchenko & Sergei Z. Levendorskiǐ, 2000. "Option Pricing For Truncated Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 549-552.
    3. Küchler, Uwe & Tappe, Stefan, 2008. "On the shapes of bilateral Gamma densities," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2478-2484, October.
    4. Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
    5. 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.
    6. 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.
    7. 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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