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On the supremum of the spectrally negative stable process with drift

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  • Coqueret, Guillaume

Abstract

We provide a series representation for the cumulative distribution of the supremum of the spectrally negative stable process with drift. We also provide two approximation methods for small and large arguments of this function. Numerical examples are detailed and a financial application is also discussed.

Suggested Citation

  • Coqueret, Guillaume, 2015. "On the supremum of the spectrally negative stable process with drift," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 333-340.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:333-340
    DOI: 10.1016/j.spl.2015.09.012
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    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    2. Kuznetsov, A., 2013. "On the density of the supremum of a stable process," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 986-1003.
    3. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    4. Guillaume Coqueret, 2013. "Lookback Option Prices Under A Spectrally Negative Tempered-Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 1-15.
    5. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.
    6. Guillaume Coqueret, 2013. "Lookback option prices under a spectrally negative tempered-stable model," Post-Print hal-02312224, HAL.
    7. Michna, Zbigniew, 2011. "Formula for the supremum distribution of a spectrally positive [alpha]-stable Lévy process," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 231-235, February.
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    Cited by:

    1. Bladt, Mogens & Ivanovs, Jevgenijs, 2021. "Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 105-123.

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