Likelihood-Based Estimation Methods for Credit Rating Stochastic Factor Model

This thesis is an empirical investigation of various estimation methods for the analysis of the dynamics of credit rating matrices. More specifically, the thesis presents three maximum likelihood estimation methods of the latent factor ordered-Probit model, which is also known as the stochastic credit migration model, a homogeneous nonlinear dynamic panel model with a common unobserved factor, to determine the dynamics of credit ratings transition probabilities. The first two methods rely on analytical approximation of the true log-likelihood function of the latent factor ordered-Probit model based on the granularity theory. The third method is maximum composite likelihood estimation of the latent factor ordered-Probit model which is the new. Chapter 1 provides the literature review on the dynamics, estimation and modelling the credit rating transition matrix. The notation and general assumptions of a latent factor ordered-Probit model are introduced, and the statistical inference of the latent factor ordered-Probit model is discussed. Chapter 2 reviews two maximum likelihood estimation methods of the latent factor ordered-Probit model which rely on analytical approximations of the log-likelihood function based on the granularity theory. The effect of the underlying state of the economy on corporate credit ratings is inferred from the common factor path. The estimated model allows us to examine the effects of shocks to the economy, i.e. the stress testing at the overall portfolio level, which is also a required element of the execution of Basel II. The stress scenarios are selected to evaluate the stressed migration probabilities and relate them with the state of the economy. The empirical results are obtained from the series of transition probabilities matrices provided by the internal rating system of a French bank over the period 2007 to 2015. Chapter 3 introduces the maximum composite likelihood estimation method for the latent factor ordered-Probit model. The computational complexity of the full information maximum likelihood in application to the stochastic migration model is the main motivation to introduce a new method, which is computationally easier and provides consistent estimators. The new method is illustrated in a simulation study that confirms good performance of the maximum composite likelihood estimation.