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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.01109 |
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| _version_ | 1866915834952155136 |
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| author | Bansal, Dhruv Goud, Mayank Majumdar, Sourav |
| author_facet | Bansal, Dhruv Goud, Mayank Majumdar, Sourav |
| contents | In the Vasicek credit portfolio model, tail risk is driven primarily by the asset-correlation parameter, yet empirically is subject to correlation risk. We propose a stochastic correlation extension of the Vasicek framework in which the correlation state evolves as a diffusion on the circle. This representation accommodates both non-mean-reverting and mean-reverting dependence regimes via circular Brownian motion and von Mises process, while retaining tractable transition densities. Conditionally on a fixed correlation state, we derive closed or semi-closed form expressions for the joint distribution of two assets, the joint first-passage (default) time distribution, and the joint survival probability. A simulation study quantifies how correlation volatility and persistence reshape joint default-at-horizon, survival, and joint barrier-crossing probabilities beyond marginal volatility effects. An empirical illustration using U.S. bank charge-off rates demonstrates economically interpretable time-variation in a dependence index and shows how inferred stochastic dependence translates into materially different joint tail-event probabilities. Overall, circular diffusion models provide a parsimonious and operationally tractable route to incorporating correlation risk into Vasicek structural credit calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01109 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A stochastic correlation extension of the Vasicek credit risk model Bansal, Dhruv Goud, Mayank Majumdar, Sourav Risk Management In the Vasicek credit portfolio model, tail risk is driven primarily by the asset-correlation parameter, yet empirically is subject to correlation risk. We propose a stochastic correlation extension of the Vasicek framework in which the correlation state evolves as a diffusion on the circle. This representation accommodates both non-mean-reverting and mean-reverting dependence regimes via circular Brownian motion and von Mises process, while retaining tractable transition densities. Conditionally on a fixed correlation state, we derive closed or semi-closed form expressions for the joint distribution of two assets, the joint first-passage (default) time distribution, and the joint survival probability. A simulation study quantifies how correlation volatility and persistence reshape joint default-at-horizon, survival, and joint barrier-crossing probabilities beyond marginal volatility effects. An empirical illustration using U.S. bank charge-off rates demonstrates economically interpretable time-variation in a dependence index and shows how inferred stochastic dependence translates into materially different joint tail-event probabilities. Overall, circular diffusion models provide a parsimonious and operationally tractable route to incorporating correlation risk into Vasicek structural credit calculations. |
| title | A stochastic correlation extension of the Vasicek credit risk model |
| topic | Risk Management |
| url | https://arxiv.org/abs/2603.01109 |