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<p>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 Lévy processes. To complement the theoretical findings, we provide numerical analysis.</p>

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Pricing American options time-capped by a drawdown event

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月25日

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  • Zbigniew Palmowski,
  • Paweł Stȩpniak

摘要

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 Lévy processes. To complement the theoretical findings, we provide numerical analysis.