  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.
