Abstract

Rating migration matrix is a crux to assess credit risks. Modeling and predicting these matrices are then an issue of great importance for risk managers in any financial institution. As a challenger to usual parametric modeling approaches, we propose a new structured dictionary learning model with auto-regressive regularization that is able to meet key expectations and constraints: small amount of data, fast evolution in time of these matrices, economic interpretability of the calibrated model. To show the model applicability, we present a numerical test with both synthetic and real data and a comparison study with the widely used parametric Gaussian Copula model: it turns out that our new approach based on dictionary learning significantly outperforms the Gaussian Copula model.

中文翻译：

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用于信用风险建模的评级迁移矩阵的结构化字典学习

摘要

评级迁移矩阵是评估信用风险的关键。对于任何金融机构的风险管理者来说，对这些矩阵进行建模和预测都是一个非常重要的问题。作为通常参数建模方法的挑战者，我们提出了一种具有自回归正则化的新结构化字典学习模型，该模型能够满足关键期望和约束：数据量小、这些矩阵随时间的快速演化、校准后的经济可解释性模型。为了展示模型的适用性，我们对合成数据和真实数据进行了数值测试，并与广泛使用的参数高斯 Copula 模型进行了比较研究：事实证明，我们基于字典学习的新方法明显优于高斯 Copula 模型。