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Last passage American cancellable option in L\'evy models

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  • Zbigniew Palmowski
  • Pawe{l} Stk{e}pniak

Abstract

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

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  • Zbigniew Palmowski & Pawe{l} Stk{e}pniak, 2022. "Last passage American cancellable option in L\'evy models," Papers 2212.01119, arXiv.org.
    • Handle: RePEc:arx:papers:2212.01119
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    References listed on IDEAS

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    1. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    2. Jevgenijs Ivanovs, 2021. "On scale functions for Lévy processes with negative phase-type jumps," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 3-19, June.
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