Pricing American Options Time-Capped by a Drawdown Event

Zbigniew Palmowski; Paweł Stȩpniak

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arXiv · 2509.00999

Pricing American Options Time-Capped by a Drawdown Event

Zbigniew Palmowski·Paweł Stȩpniak

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

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Zbigniew Palmowski, Paweł Stȩpniak. 2025-08-31. Pricing American Options Time-Capped by a Drawdown Event. https://arxiv.org/abs/2509.00999

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