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摘要翻译：
在企业对数杠杆率为时变布朗运动(TCBM)的重要特殊情况下，我们考虑了结构信用模型，将时变视为一个独立的增长过程。遵循布莱克和考克斯的方法，一种将违约时间定义为对数杠杆率超过零水平的第一个通过时间。我们不采用第一次通过的经典概念及其相关的数字挑战，而是接受一种适用于技术和建立信任措施的替代概念，称为“第二类第一次通过”。我们演示了如何在这类新模型中有效地实现统计推断。这使得我们可以比较两个版本的TCBMs的性能，方差伽马(VG)模型和指数跳跃模型(EXP)与Black-Cox模型。当应用于福特汽车（Ford Motor Co.）长达4.5年的每周信用违约互换(CDS)报价数据集时，得出的结论是，两个TCBM模型，本质上只有一个额外的参数，可以显著优于经典的Black-Cox模型。
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英文标题：
《Statistical Inference for Time-changed Brownian Motion Credit Risk
Models》
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作者：
T. R. Hurd and Zhuowei Zhou
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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PDF链接：
https://arxiv.org/pdf/1102.2412
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