Pricing American Options Time-Capped by a Drawdown Event

2025/08/31 by Zbigniew Palmowski, Palmowski, Zbigniew, Paweł Stȩpniak +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #Diffusion and Search Dynamics #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2509.00999

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• American Options with Last Exit Times: A Free-Boundary Approach
• Defaultable perpetual Russian option Under a last passage time model
• Fair valuation of L 'evy-type drawdown-drawup contracts with general\n insured and penalty functions
• Pricing insurance drawdown-type contracts with underlying Lévy assets
• On the drawdown of completely asymmetric Levy processes
• Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups

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