Corporate Probability of Default: A Single-Index Hazard Model Approach
提出一个灵活且易解释的单指数风险模型来预测企业违约概率，发现违约概率与协变量呈V形关系，且模型校准优于线性风险模型，在经济价值分析中利润可达线性模型的三倍。
Corporate probability of default (PD) prediction is vitally important for risk management and asset pricing. In search of accurate PD prediction, we propose a flexible yet easy-to-interpret default-prediction single-index hazard model (DSI). By applying it to a comprehensive U.S. corporate bankruptcy database we constructed, we discover an interesting V-shaped relationship, indicating a violation of the common linear hazard specification. Most importantly, the single-index hazard model passes the Hosmer-Lemeshow goodness-of-fit calibration test while neither does a state-of-the-art linear hazard model in finance nor a parametric class of Box-Cox transformation survival models. In an economic value analysis, we find that this may translate to as much as three times of profit compared to the linear hazard model. In model estimation, we adopt a penalized-spline approximation for the unknown function and propose an efficient algorithm. With a diverging number of spline knots, we establish consistency and asymptotic theories for the penalized-spline likelihood estimators. Furthermore, we reexamine the distress risk anomaly, that is, higher financially distressed stocks deliver anomalously lower excess returns. Based on the PDs from the proposed single-index hazard model, we find that the distress risk anomaly has weakened or even disappeared during the extended period.