A stochastic correlation extension of the Vasicek credit risk model
In this paper we extend the Vasicek credit risk model by modelling the correlation as a continuous-time process. The models for correlation follow diffusion processes on the circle. In particular we work with the Circular Brownian motion and a mean-reverting von Mises process. The analytical and computational tractability of these circular diffusion enables us to derive terminal asset and loss distributions by averaging their conditional laws over the law of time-averaged correlation, and evaluate path-dependent probabilities by Monte Carlo simulation. Simulations distinguish terminal joint default, joint survival, first-to-default, and joint first passage, and show how stochastic correlation reallocates probability between concordant and discordant outcomes. We fit both specifications to U.S. bank charge-off data, demonstrating that the framework remains tractable for probabilistic analysis and statistical estimation.