摘要翻译：
第一次通过模型提供了一个很有吸引力的框架来建模违约过程，其中公司资产经历相关的随机游动，如果公司的资产低于阈值，公司就会违约。典型的一年期违约相关性很小，即只有百分之几，但对于管理投资组合信用风险和一些信用衍生品定价（例如first to default Basks）来说，包括相关性非常重要。在第一阶段模型中，两个以上企业的联合生存概率对其资产相关性的确切依赖关系是未知的。利用关联中的一阶扰动理论，导出了n美元企业联合生存概率与资产关联的关系表达式。它包括了相关中所有线性项，但忽略了二次和高阶项的影响。对于恒定时间无关的相关性，我们将关节存活概率的第一次传递模型表达式与多元正态Copula函数给出的结果进行了比较。作为我们结果的一个实际应用，我们计算了五个基本工业的五年联合生存概率对其资产相关性的依赖关系。
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英文标题：
《Correlated Random Walks and the Joint Survival Probability》
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作者：
Mark B. Wise and Vineer Bhansali
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最新提交年份：
2008
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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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英文摘要：
  First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations are small, i.e., of order a few percent, but nonetheless including correlations is very important, for managing portfolio credit risk and pricing some credit derivatives (e.g. first to default baskets). In first passage models the exact dependence of the joint survival probability of more than two firms on their asset correlations is not known. We derive an expression for the dependence of the joint survival probability of $n$ firms on their asset correlations using first order perturbation theory in the correlations. It includes all terms that are linear in the correlations but neglects effects of quadratic and higher order. For constant time independent correlations we compare the first passage model expression for the joint survival probability with what a multivariate normal Copula function gives. As a practical application of our results we calculate the dependence of the five year joint survival probability for five basic industrials on their asset correlations.
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PDF链接：
https://arxiv.org/pdf/0812.2000