Structural Credit Risk Model with Stochastic Volatility: A Particle-filter Approach

This paper extends Merton's structural credit risk model to account for the fact that the firm's asset volatility follows a stochastic process. With the presence of stochastic volatility, the transformed-data maximum likelihood estimation (MLE) method of Duan (1994, 2000) can no longer be applied to estimate the model. We devise a particle filtering algorithm to solve this problem. This algorithm is based on the general non-linear and non-Gaussian filtering with sequential parameter learning, and a simulation study is conducted to ascertain its finite sample performance. Meanwhile, we implement this model on the real data of companies in Dow Jones industrial average and find that incorporating stochastic volatility into the structural model can largely improve the model performance.