Year: 2025
Type: article
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.
Authors: Zbigniew Palmowski, Paweł Stȩpniak
Institution: Wrocław University of Science and Technology
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Award: G678311281
OpenAlex ID: W4416616946