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Exponential stock models driven by tempered stable processes

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  • Küchler, Uwe
  • Tappe, Stefan

Abstract

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy 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.

Suggested Citation

  • Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, vol. 181(1), pages 53-63.
    • Handle: RePEc:eee:econom:v:181:y:2014:i:1:p:53-63
    DOI: 10.1016/j.jeconom.2014.02.008
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    References listed on IDEAS

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    1. Küchler, Uwe & Tappe, Stefan, 2008. "Bilateral gamma distributions and processes in financial mathematics," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 261-283, February.
    2. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    3. Küchler Uwe & Tappe Stefan, 2009. "Option pricing in bilateral Gamma stock models," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 281-307, December.
    4. 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.
    5. Küchler, Uwe & Tappe, Stefan, 2008. "On the shapes of bilateral Gamma densities," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2478-2484, October.
    6. Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
    7. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    8. 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.
    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. Olivier Le Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Post-Print hal-02312142, HAL.
    2. Lorenzo Mercuri & Edit Rroji, 2018. "Risk parity for Mixed Tempered Stable distributed sources of risk," Annals of Operations Research, Springer, vol. 260(1), pages 375-393, January.
    3. Ripamonti, Alexandre & Silva, Diego & Moreira Neto, Eurico, 2018. "Asset Pricing and Asymmetric Information," MPRA Paper 87403, University Library of Munich, Germany.
    4. 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.
    5. Olivier Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(2), pages 87-109, June.
    6. Yunfei Xia & Michael Grabchak, 2024. "Pricing multi-asset options with tempered stable distributions," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-24, December.
    7. Lorenzo Mercuri & Edit Rroji, 2014. "Parametric Risk Parity," Papers 1409.7933, arXiv.org.

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