Composite Likelihood for Stochastic Migration Model with Unobserved Factor

TL;DR

This paper proposes a new composite likelihood estimation method for a stochastic credit rating transition model, improving accuracy and robustness in regulatory risk assessment.

Contribution

It introduces the conditional Maximum Composite Likelihood estimator for the factor ordered Probit model, addressing issues with likelihood approximation sensitivity.

Findings

The proposed estimators are consistent and asymptotically normal.

Simulation studies show improved finite-sample performance.

Empirical application demonstrates practical usefulness.

Abstract

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.