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Optimal Multiple Stopping And Valuation Of Swing Options In Lévy Models

Author

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  • AMINA BOUZGUENDA ZEGHAL

    (ENIT-LAMSIN, B.P. 37, 1002 Tunis-Belvédère, Tunisie)

  • MOHAMED MNIF

    (ENIT-LAMSIN, B.P. 37, 1002 Tunis-Belvédère, Tunisie)

Abstract

In this paper, we extend the results of Carmona and Touzi [6] for an optimal multiple stopping problem to a market where the price process is allowed to jump. We also generalize the problem of valuation swing options to the context of a Lévy market. We prove the existence of multiple exercise policies under an additional condition on Snell envelops. This condition emerges naturally in the case of Lévy processes. Then, we give a constructive solution for perpetual put swing options when the price process has no negative jumps. We use the Monte Carlo approximation method based on Malliavin calculus in order to solve the finite horizon case. Numerical results are given in the last two sections. We illustrate the theoretical results of the perpetual case and give the numerical solution for the finite horizon case.

Suggested Citation

  • Amina Bouzguenda Zeghal & Mohamed Mnif, 2006. "Optimal Multiple Stopping And Valuation Of Swing Options In Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1267-1297.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:08:n:s0219024906004037
    DOI: 10.1142/S0219024906004037
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    Citations

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    Cited by:

    1. S. C. P. Yam & W. Zhou, 2017. "Optimal Liquidation of Child Limit Orders," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 517-545, May.
    2. J. Lars Kirkby & Shi-Jie Deng, 2019. "Swing Option Pricing By Dynamic Programming With B-Spline Density Projection," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-53, December.
    3. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    4. Mingsi Long & Hongzhong Zhang, 2017. "On the optimality of threshold type strategies in single and recursive optimal stopping under L\'evy models," Papers 1707.07797, arXiv.org, revised Aug 2018.
    5. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
    6. Christian Bender & Nikolai Dokuchaev, 2013. "A First-Order BSPDE for Swing Option Pricing," Papers 1305.3988, arXiv.org.
    7. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    8. Long, Mingsi & Zhang, Hongzhong, 2019. "On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2821-2849.
    9. Imene Ben Latifa & Joseph Frederic Bonnans & Mohamed Mnif, 2011. "Optimal multiple stopping problem and financial applications," Working Papers hal-00642919, HAL.

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