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Pricing American Options Time-Capped by a Drawdown Event

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

Abstract

This paper presents a derivation of the explicit price for the perpetual American put option in the Black-Scholes model, time-capped by the first drawdown epoch beyond a predefined level. We demonstrate that the optimal exercise strategy involves executing the option when the asset price first falls below a specified threshold. The proof relies on martingale arguments and the fluctuation theory of L\'evy processes. To complement the theoretical findings, we provide numerical analysis.

Suggested Citation

  • Zbigniew Palmowski & Pawe{l} Stc{e}pniak, 2025. "Pricing American Options Time-Capped by a Drawdown Event," Papers 2509.00999, arXiv.org.
    • Handle: RePEc:arx:papers:2509.00999
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    File URL: http://arxiv.org/pdf/2509.00999
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