Bayesian Analysis of Structural Credit Risk Models with Microstructure Noises

In this paper a Markov chain Monte Carlo (MCMC) technique is developed for the Bayesian analysis of structural credit risk models with microstruc- ture noises. The technique is based on the general Bayesian approach with posterior computations performed by Gibbs sampling. Simulations from the Markov chain, whose stationary distribution converges to the posterior distri- bution, enable exact finite sample inferences of model parameters. The exact inferences can easily be extended to latent state variables and any nonlinear transformation of state variables and parameters, facilitating practical credit risk applications. In addition, the comparison of alternative models can be based on deviance information criterion (DIC) which is straightforwardly ob- tained from the MCMC output. The method is implemented on the basic structural credit risk model with pure microstructure noises and some more general specifications using daily equity data from US and emerging mar- kets. We find empirical evidence that microstructure noises are positively correlated with the firm values in emerging markets.