Last-Passage American Cancelable Option in Lévy Models

Zbigniew Palmowski () and Paweł Stȩpniak
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Zbigniew Palmowski: Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-372 Wrocław, Poland
Paweł Stȩpniak: Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-372 Wrocław, Poland

JRFM, 2023, vol. 16, issue 2, 1-14

Abstract: We derive the explicit price of the perpetual American put option canceled at the last-passage time of the underlying above some fixed level. We assume that the asset process is governed by a geometric spectrally negative Lévy process. We show that the optimal exercise time is the first moment when the asset price process drops below an optimal threshold. We perform numerical analysis considering classical Black–Scholes models and the model where the logarithm of the asset price has additional exponential downward shocks. The proof is based on some martingale arguments and the fluctuation theory of Lévy processes.

Keywords: American options; optimal stopping problem; Lévy process; last passage time; free boundary problem (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
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