A stochastic correlation extension of the Vasicek credit risk model

TL;DR

This paper introduces a stochastic correlation extension to the Vasicek credit risk model, capturing correlation dynamics as a diffusion process on the circle, improving tail risk assessment and dependence modeling.

Contribution

It develops a novel circular diffusion framework for stochastic correlation in the Vasicek model, enabling tractable analysis of joint default probabilities with time-varying dependence.

Findings

Correlation volatility significantly affects joint default probabilities.

Empirical application shows time-varying dependence impacts tail-event risk.

Model provides a practical way to incorporate correlation risk into credit calculations.

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.