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摘要翻译：
t copula常用于风险管理中，因为它可以模拟风险之间的尾部依赖关系，并且很容易模拟和校准。然而，标准t copula的使用常常受到批评，因为它对自由度有一个单一参数的限制，这可能限制了它在多变量情况下建模尾部依赖结构的能力。为了克服这一问题，最近提出了分组t copula，即先验地对风险进行分组，使每组风险都有一个标准的t copula及其特定的自由度参数。在本文中，我们提出了一个分组t copula，其中每个组只包含一个风险因子，因此不需要先验分组。研究了二元情形下的copula特征。我们解释了模拟和校准过程，包括对最大似然估计和Kendall的tau近似的有限样本性质的模拟研究。这种新的copula在风险度量方面与标准的t copula有显著的不同，如尾部依赖、在险价值和预期缺口。关键词：分组t系词，尾部依赖，风险管理。
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英文标题：
《The t copula with Multiple Parameters of Degrees of Freedom: Bivariate
Characteristics and Application to Risk Management》
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作者：
Xiaolin Luo and Pavel V. Shevchenko
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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：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：
The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula can be significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall. Keywords: grouped t copula, tail dependence, risk management.
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PDF链接：
https://arxiv.org/pdf/0710.3959
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