Estimating Jump Diffusion Structural Credit Risk Models

There is strong evidence that structural models of credit risk significantly underestimate both credit yield spreads and the probability of default if the value of corporate assets follows a diffusion process. Adding a jump component to the firm value process is a potential remedy for the underestimation. However, there are very few empirical studies of jump-diffusion (or Levy) structural models in the literature. The major challenge is the estimation of hidden variables, such as the firm value, volatility, and parameters of the jump component, as the value of corporate assets is not directly observable. In practice, parameters and the value of the firm should be estimated using the market values of equities. This paper provides a promising estimation method for jump-diffusion processes in structural models that are based on observed stock data. We show that the traditional estimation methods for structural models, the variance-restriction method and maximum likelihood estimation, fail when jumps appear in credit risk models. We then propose a penalized likelihood approach and devise a corresponding expectationmaximum algorithm. The approach is applied to the jump-diffusion processes of Merton (1976) and Kou (2002) and the performance is examined through a series of simulations and empirical data. JEL classification: To be determined