Paper: arXiv 2603.01109

Authors: Dhruv Bansal, Mayank Goud, Sourav Majumdar

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative circular diffusion parameterization for stochastic asset correlation in structural credit models, maintaining geometric boundedness by design. It delivers solid mathematical derivations (first-passage times, Laplace approximations) alongside both simulation studies and empirical application to US bank charge-off data.

Research Flowchart

  flowchart TD
    A[Research Goal: Incorporate Correlation Risk into Vasicek Model] --> B[Model Formulation: Circular Diffusion on the Circle]
    B --> C[Derive Conditional Joint Default Times & Survival Probabilities]
    D[Inputs: U.S. Bank Charge-off Data & Volatility Parameters] --> E[Simulation Study & Empirical Parameter Inference]
    C --> E
    E --> F[Key Outcome: Time-varying Dependence & Reshaped Joint Tail Risk]

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1 of 48 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.