In this dissertation we: (1) develop a statistical framework for testing dependence assumptions in a given time series; (2) develop a statistical test for comparing dependence structures (aka copula functions ) derived from the Normal and Student-t distributions and use this to quantify the potential for extreme co-movements and; (3) analyze in detail credit derivative models and their sensitivity to different dependence assumptions.; The main results of our studies may be summarized as follows. First, the t-copula assumption is a more plausible model of dependence for the tested time-series; the Normal copula provides a lesser fit than the t-copula but a superior fit compared with the three Archimedean copulas tested, namely, Frank, Gumbel, and Clayton. Second, exploiting the nesting of the Normal copula within the t-family we show that the former can be almost always rejected on the basis of a likelihood ratio test. Third, financial data exhibit a clear tendency for extreme co-movements which cannot be predicted on the basis of a Normal copula model. Fourth, as the dimensionality increases (i.e., the number of assets being tested for dependence increases) the distinction between the Normal and t-copulas become “sharper”. Fifth, the dependence structure of asset returns is strikingly similar to the one underlying equity returns. Finally, the tendency for extreme co-movements does not seem to be affected by the sampling frequency, in contrast to the phenomenon observed in univariate returns that tend to be “heavy-tailed” in higher frequencies, and more “Gaussian-like” in lower frequencies.; Our results bear important financial implications which we illustrate throughout this thesis with examples that include: MSCI national equity indices data; risk measure for portfolios of equity options; pricing n th to default baskets; pricing and risk measures of synthetic CDO tranches, and; analysis of portfolio tail dependence indices.
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机译:在本文中,我们:(1)建立一个统计框架以测试给定时间序列中的依赖假设; (2)开发统计测试,以比较从正态分布和Student- t italic>分布得出的依存结构(又称 copula函数 italic>),并以此量化潜在的极端共动作; (3)详细分析信用衍生工具模型及其对不同依赖假设的敏感性。我们研究的主要结果可以总结如下。首先, t italic> -copula假设是一个更合理的依赖关系模型,用于测试时间序列;与 t italic> -copula相比,Normal copula的拟合度较小,但与测试的三种Archimedean copulas,即Frank,Gumbel和Clayton相比,拟合度更高。第二,利用正常系鸡在 t italic>族中的筑巢,我们表明,在似然比检验的基础上,前者几乎总是可以被拒绝的。第三,财务数据显示出极端共同运动的明显趋势,这是无法基于正态copula模型进行预测的。第四,随着维数的增加(即,要测试依赖关系的资产数量增加),普通和 -copitals之间的区别变得更“犀利”。第五,资产收益率 italic>的依存结构非常类似于一种基础的股权收益率 italic>。最后,极端共同运动的趋势似乎不受采样频率的影响,这与单变量收益率中观察到的现象相反,后者在较高的频率中往往“重尾”,而在较高的频率中更像“高斯型”。较低的频率。我们的结果具有重要的财务意义,我们将在整个论文中用以下示例进行说明:MSCI国家股票指数数据;股票期权投资组合的风险衡量;将n th super> italic>定价为默认购物篮;合成CDO档的定价和风险衡量;以及投资组合尾部依赖指数的分析。
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