多变量默认时间的一致迭代模拟：a 马尔可夫指标表征

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摘要翻译：
我们研究了在什么条件下，在最终时间范围内对联合违约时间的单个模拟可以分解为在随后的相邻子周期上对导致该最终时间范围的联合违约时间的一组模拟。除了理论上的利益，这也是一个实际问题，因为行业的一部分一直在误导性的假设下工作，认为这两种方法在实际目的上是等同的。作为现实程式化事实、实际需求和数学可处理性之间的合理权衡，我们提出了导致马尔可夫多变量生存指标过程的模型，并从统计文献中研究了违约时间向量的两个静态模型实例，它们属于这一类。一方面，已知“循环缺省”情形具有这种性质，并指出它与二元情形下的经典“弗氏分布”相吻合。另一方面，如果生存指标过程的所有子向量都是马尔可夫的，这就构成了马歇尔-奥尔金分布的新特征，因此也就构成了多变量记忆缺失的新特征。所得到的模型的一个最重要的性质是多元分布类型的稳定性，关于消除或插入一个具有同一族边际分布的新边际分量。这种“嵌套边距”属性的实际含义是巨大的。为了实现这种分布，我们提出了一种基于L\'evy-failty结构的高效无偏仿真算法。我们强调了不同的陷阱在模拟依赖的默认时间，并检查，在一个数值案例研究中，不充分的模拟实践的影响。
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英文标题：
《Consistent iterated simulation of multi-variate default times: a
  Markovian indicators characterization》
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作者：
Damiano Brigo, Jan-Frederik Mai, Matthias Scherer
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最新提交年份：
2014
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  We investigate under which conditions a single simulation of joint default times at a final time horizon can be decomposed into a set of simulations of joint defaults on subsequent adjacent sub-periods leading to that final horizon. Besides the theoretical interest, this is also a practical problem as part of the industry has been working under the misleading assumption that the two approaches are equivalent for practical purposes. As a reasonable trade-off between realistic stylized facts, practical demands, and mathematical tractability, we propose models leading to a Markovian multi-variate survival--indicator process, and we investigate two instances of static models for the vector of default times from the statistical literature that fall into this class. On the one hand, the "looping default" case is known to be equipped with this property, and we point out that it coincides with the classical "Freund distribution" in the bivariate case. On the other hand, if all sub-vectors of the survival indicator process are Markovian, this constitutes a new characterization of the Marshall--Olkin distribution, and hence of multi-variate lack-of-memory. A paramount property of the resulting model is stability of the type of multi-variate distribution with respect to elimination or insertion of a new marginal component with marginal distribution from the same family. The practical implications of this "nested margining" property are enormous. To implement this distribution we present an efficient and unbiased simulation algorithm based on the L\'evy-frailty construction. We highlight different pitfalls in the simulation of dependent default times and examine, within a numerical case study, the effect of inadequate simulation practices.
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PDF链接：
https://arxiv.org/pdf/1306.0887

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关键词：马尔可夫 多变量 distribution Quantitative Applications 时间 simulation property 等同 边际