Abstract
We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein–Uhlenbeck process, a diffusion often adopted by practitioners to model commodity prices and interest rates. By framing the optimal exercise of the American option as a problem of optimal stopping and relying on probabilistic arguments, we provide a non-linear Volterra-type integral equation characterizing the exercise boundary, develop a novel comparison argument to derive upper and lower bounds for such a boundary, and prove its Lipschitz continuity in any closed interval that excludes the expiration date and, thus, its differentiability almost everywhere. We implement a Picard iteration algorithm to solve the Volterra integral equation and show illustrative examples that shed light on the boundary's dependence on the process's drift and volatility.
Acknowledgments
The authors acknowledge the comments of two anonymous referees that led to significant improvements in the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Correction Statement
This article has been corrected with minor changes. These changes do not impact the academic content of the article.