Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909221288673280 |
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| author | Azze, Abel D'Auria, Bernardo García-Portugués, Eduardo |
| author_facet | Azze, Abel D'Auria, Bernardo García-Portugués, Eduardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04095 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes Azze, Abel D'Auria, Bernardo García-Portugués, Eduardo Probability Mathematical Finance Pricing of Securities 60G40, 60J60 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. |
| title | Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes |
| topic | Probability Mathematical Finance Pricing of Securities 60G40, 60J60 |
| url | https://arxiv.org/abs/2211.04095 |