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Double continuation regions for American and Swing options with negative discount rate in Lévy models

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  • Marzia De Donno
  • Zbigniew Palmowski
  • Joanna Tumilewicz

Abstract

In this paper, we study perpetual American call and put options in an exponential Lévy model. We consider a negative effective discount rate that arises in a number of financial applications including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount factor. We show that in this case a double continuation region arises and we identify the two critical prices. We also generalize this result to multiple stopping problems of Swing type, that is, when successive exercise opportunities are separated by i.i.d. random refraction times. We conduct an extensive numerical analysis for the Black–Scholes model and the jump‐diffusion model with exponentially distributed jumps.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:1:p:196-227
    DOI: 10.1111/mafi.12218
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    1. Detemple, Jérôme & Laminou Abdou, Souleymane & Moraux, Franck, 2020. "American step options," European Journal of Operational Research, Elsevier, vol. 282(1), pages 363-385.
    2. Anna Battauz & Marzia De Donno & Janusz Gajda & Alessandro Sbuelz, 2022. "Optimal exercise of American put options near maturity: A new economic perspective," Review of Derivatives Research, Springer, vol. 25(1), pages 23-46, April.
    3. Jonas Al-Hadad & Zbigniew Palmowski, 2020. "Perpetual American options with asset-dependent discounting," Papers 2007.09419, arXiv.org, revised Jan 2021.
    4. Battauz, Anna & De Donno, Marzia & Sbuelz, Alessandro, 2022. "On the exercise of American quanto options," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    5. Gapeev, Pavel V., 2020. "Optimal stopping problems for running minima with positive discounting rates," LSE Research Online Documents on Economics 105849, London School of Economics and Political Science, LSE Library.
    6. Ludovic Mathys, 2019. "Valuing Tradeability in Exponential L\'evy Models," Papers 1912.00469, arXiv.org, revised Feb 2020.
    7. Zbigniew Palmowski & José Luis Pérez & Kazutoshi Yamazaki, 2021. "Double continuation regions for American options under Poisson exercise opportunities," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 722-771, April.
    8. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    9. Jonas Al-Hadad & Zbigniew Palmowski, 2021. "Pricing Perpetual American Put Options with Asset-Dependent Discounting," JRFM, MDPI, vol. 14(3), pages 1-19, March.

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