Composite Likelihood for Stochastic Migration Model with Unobserved Factor
针对银行内部信用评级迁移的随机因子有序Probit模型，提出条件最大复合似然估计法，避免高维积分近似导致的统计监管套利，并证明估计量的一致性和渐近正态性。
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.