Multiple Stopping and Exercise Boundaries for American Put Options
Abstract
This article studies a finite-horizon American put option with up to m exercise rights under the risk-neutral Black--Scholes model, where consecutive exercises must be separated by a prescribed refractory period δ>0 and unused rights may expire. For each number of remaining rights, we show that optimal exercise is characterized by a single exercise boundary and that these boundaries are ordered by the number of remaining rights. We prove optimality of the first boundary-hitting time and establish local Lipschitz continuity of the exercise boundaries within each open deadline strip. Away from the deadlines, we derive smooth fit, the associated quasi-variational inequality and free-boundary formulation, an early-exercise-premium representation, recursive Volterra-type boundary equations, and a verification theorem. We also extend the recursive formulation to an independent random termination time, thereby allowing for exogenous termination of the option contract.
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BibTeX
@misc{ano2026multiple,
title = {{Multiple Stopping and Exercise Boundaries for American Put Options}},
author = {Katsunori Ano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30637},
eprint = {2610.30637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30637},
}
RIS
TY - UNPB
TI - Multiple Stopping and Exercise Boundaries for American Put Options
AU - Katsunori Ano
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30637
UR - https://arxiv.org/abs/2610.30637
AB - This article studies a finite-horizon American put option with up to m exercise rights under the risk-neutral Black--Scholes model, where consecutive exercises must be separated by a prescribed refractory period δ>0 and unused rights may expire. For each number of remaining rights, we show that optimal exercise is characterized by a single exercise boundary and that these boundaries are ordered by the number of remaining rights. We prove optimality of the first boundary-hitting time and establish local Lipschitz continuity of the exercise boundaries within each open deadline strip. Away from the deadlines, we derive smooth fit, the associated quasi-variational inequality and free-boundary formulation, an early-exercise-premium representation, recursive Volterra-type boundary equations, and a verification theorem. We also extend the recursive formulation to an independent random termination time, thereby allowing for exogenous termination of the option contract.
ER -