Composite Likelihood for Stochastic Migration Model with Unobserved Factor

We introduce the conditional Maximum Composite Likelihood (MCL) estimation method for the stochastic factor ordered Probit model of credit rating transitions of firms. This model is recommended for internal credit risk assessment procedures in banks and financial institutions under the Basel III regulations. Its exact likelihood function involves a high-dimensional integral, which can be approximated numerically before maximization. However, the estimated migration risk and required capital tend to be sensitive to the quality of this approximation, potentially leading to statistical regulatory arbitrage. The proposed conditional MCL estimator circumvents this problem and maximizes the composite log-likelihood of the factor ordered Probit model. We present three conditional MCL estimators of different complexity and examine their consistency and asymptotic normality when n and T tend to infinity. The performance of these estimators at finite T is examined and compared with a granularity-based approach in a simulation study. The use of the MCL estimator is also illustrated in an empirical application

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