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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.11619 |
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| _version_ | 1866929741838155776 |
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| author | Fontana, Claudio Lanaro, Giacomo Murgoci, Agatha |
| author_facet | Fontana, Claudio Lanaro, Giacomo Murgoci, Agatha |
| contents | We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Björk and co-authors in the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model can be realized by a finite-dimensional state process. We illustrate the general theory in a number of model classes and examples, providing explicit constructions of finite-dimensional realizations. Based on these theoretical results, we perform the calibration of a three-curve Hull-White model to market data and analyse the stability of the estimated parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The geometry of multi-curve interest rate models Fontana, Claudio Lanaro, Giacomo Murgoci, Agatha Mathematical Finance 60H15, 91G30 We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Björk and co-authors in the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model can be realized by a finite-dimensional state process. We illustrate the general theory in a number of model classes and examples, providing explicit constructions of finite-dimensional realizations. Based on these theoretical results, we perform the calibration of a three-curve Hull-White model to market data and analyse the stability of the estimated parameters. |
| title | The geometry of multi-curve interest rate models |
| topic | Mathematical Finance 60H15, 91G30 |
| url | https://arxiv.org/abs/2401.11619 |