Pricing American Options Time-Capped by a Drawdown Event
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909763503128576 |
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| author | Palmowski, Zbigniew Stȩpniak, Paweł |
| author_facet | Palmowski, Zbigniew Stȩpniak, Paweł |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pricing American Options Time-Capped by a Drawdown Event Palmowski, Zbigniew Stȩpniak, Paweł Mathematical Finance Probability 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. |
| title | Pricing American Options Time-Capped by a Drawdown Event |
| topic | Mathematical Finance Probability |
| url | https://arxiv.org/abs/2509.00999 |