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Last-Passage American Cancelable Option in Lévy Models

Author

Listed:
  • Zbigniew Palmowski

    (Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-372 Wrocław, Poland)

  • Paweł Stȩpniak

    (Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-372 Wrocław, Poland)

Abstract

We derive the explicit price of the perpetual American put option canceled at the last-passage time of the underlying above some fixed level. We assume that the asset process is governed by a geometric spectrally negative Lévy process. We show that the optimal exercise time is the first moment when the asset price process drops below an optimal threshold. We perform numerical analysis considering classical Black–Scholes models and the model where the logarithm of the asset price has additional exponential downward shocks. The proof is based on some martingale arguments and the fluctuation theory of Lévy processes.

Suggested Citation

  • Zbigniew Palmowski & Paweł Stȩpniak, 2023. "Last-Passage American Cancelable Option in Lévy Models," JRFM, MDPI, vol. 16(2), pages 1-14, January.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:2:p:82-:d:1050619
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    References listed on IDEAS

    as
    1. Alex Szimayer, 2005. "Valuation of American options in the presence of event risk," Finance and Stochastics, Springer, vol. 9(1), pages 89-107, January.
    2. Pavel V. Gapeev & Peter M. Kort & Maria N. Lavrutich & Jacco J. J. Thijssen, 2022. "Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 789-813, June.
    3. Pavel V. Gapeev & Hessah Al Motairi, 2018. "Perpetual American Defaultable Options in Models with Random Dividends and Partial Information," Risks, MDPI, vol. 6(4), pages 1-15, November.
    Full references (including those not matched with items on IDEAS)

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