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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/2410.08808 |
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| _version_ | 1866912069350064128 |
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| author | Keller-Ressel, Martin Sachse, Felix |
| author_facet | Keller-Ressel, Martin Sachse, Felix |
| contents | We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics further restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. Moreover a single shape (either inverse of normal curves) must dominate in the long-run. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08808 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Term structure shapes and their consistent dynamics in the Svensson family Keller-Ressel, Martin Sachse, Felix Mathematical Finance Theoretical Economics Dynamical Systems 91G30 We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics further restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. Moreover a single shape (either inverse of normal curves) must dominate in the long-run. |
| title | Term structure shapes and their consistent dynamics in the Svensson family |
| topic | Mathematical Finance Theoretical Economics Dynamical Systems 91G30 |
| url | https://arxiv.org/abs/2410.08808 |