Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes

Autor:	Azze, Abel, D'Auria, Bernardo, García-Portugués, Eduardo
Rok vydání:	2022
Předmět:	Mathematics - Probability Quantitative Finance - Mathematical Finance Quantitative Finance - Pricing of Securities 60G40 60J60
Zdroj:	Stochastics, 96(1):921-946, 2024
Druh dokumentu:	Working Paper
DOI:	10.1080/17442508.2024.2325402
Popis:	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. Comment: 25 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.04095 Zobrazit plný text záznamu View this record from Arxiv