含未观测因子的随机迁移模型的复合似然估计
Composite Likelihood for Stochastic Migration Model with Unobserved Factor
AI总结：
本文提出条件最大复合似然（MCL）估计方法，用于含未观测因子的随机有序Probit信用评级迁移模型，以避免高维积分近似导致的监管套利，并证明其一致性与渐近正态性。
摘要：
我们针对企业信用评级转移的随机因子有序Probit模型，引入了条件最大复合似然（MCL）估计方法。该模型被推荐用于巴塞尔III监管框架下银行和金融机构的内部信用风险评估程序。其精确似然函数涉及高维积分，可在最大化前进行数值近似。然而，估计的迁移风险和所需资本往往对该近似的质量敏感，可能导致统计监管套利。所提出的条件MCL估计器规避了这一问题，并最大化因子有序Probit模型的复合对数似然。我们提出了三种不同复杂度的条件MCL估计器，并考察了当n和T趋于无穷时它们的一致性和渐近正态性。在模拟研究中，我们考察了这些估计器在有限T下的表现，并与基于粒度的方法进行了比较。此外，还在一个实证应用中展示了MCL估计器的使用。
英文摘要：
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.
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