时变布朗运动信用风险模型的统计推断
Statistical Inference for Time-changed Brownian Motion Credit Risk Models
摘要：
我们考虑了一种重要的特殊情况下的结构信用模型，即企业的对数杠杆率是一个时变布朗运动（TCBM），其中时变过程是一个独立的增长过程。按照布莱克和考克斯的方法，人们将违约时间定义为对数杠杆率首次越过零水平的时间。我们不采用传统的"第一次通过“概念及其相关的数字挑战，而是接受适用于透明度和建立信任措施的另一种概念，称为“第二类第一次通过”。我们演示了如何统计推断可以有效地实现在这一类新的模型。这使我们能够比较两个版本的透明度和建立信任措施的性能，方差伽马（VG）模型和指数跳跃模型（EXP），布莱克考克斯模型。当应用到一个为期4.5年的数据集每周信用违约互换（CDS）报价福特汽车公司，结论是，这两个TCBM模型，本质上是一个额外的参数，可以显着优于经典的布莱克考克斯模型。
英文摘要：
We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time for the log-leverage ratio to cross the level zero. Rather than adopt the classical notion of first passage, with its associated numerical challenges, we accept an alternative notion applicable for TCBMs called "first passage of the second kind". We demonstrate how statistical inference can be efficiently implemented in this new class of models. This allows us to compare the performance of two versions of TCBMs, the variance gamma (VG) model and the exponential jump model (EXP), to the Black-Cox model. When applied to a 4.5 year long data set of weekly credit default swap (CDS) quotes for Ford Motor Co, the conclusion is that the two TCBM models, with essentially one extra parameter, can significantly outperform the classic Black-Cox model.
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