How robust is the value-at-risk of credit risk portfolios?
How robust is the value-at-risk of credit risk portfolios?
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DOI：
10.1080/1351847x.2015.1104370
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发表时间：
2015-10
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影响因子：
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通讯作者：
C. Bernard;L. Rüschendorf;S. Vanduffel;Jing Yao
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文献类型：
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作者：
C. Bernard;L. Rüschendorf;S. Vanduffel;Jing Yao
在本文中，我们评估了信用风险组合模型的模型不确定性的大小，即在给定一定数量的可用信息的情况下，风险贷款组合的最大和最小风险价值（VaR）是什么。Puccetti, r<s:1> schendorf [2012a]。“相关风险函数分布的锐界计算”。[j] .数学学报（自然科学版），2013,(2):1 - 8。“模型不确定性与VaR聚合”。[j] [Journal of Banking and Finance], 37, 2750-2764]提出重排算法（RA）作为一种近似VaR边界的一般方法，当不同贷款的损失分布已知但不知道它们的相互依赖性（无约束边界）时。他们的数值结果表明，最坏情况和最佳情况VaR之间的差距通常非常大，这一特征只能通过缺乏使用依赖信息来解释。我们提出了对RA的一种修正，使得当除了边际分布之外，总投资组合的高阶矩（如方差和偏度）也可用作依赖信息来源时，可以近似尖锐的VaR边界。数值研究表明，矩信息的使用可以显著改善（无约束）VaR边界。然而，在高置信度水平下进行的信贷组合的VaR评估（如偿付能力II和巴塞尔协议III中的情况）仍然受到显著的模型不确定性的影响，并且不稳健。
In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, that is, what is the maximum and minimum value-at-risk (VaR) of a portfolio of risky loans that can be justified given a certain amount of available information. Puccetti and Rüschendorf [2012a. “Computation of Sharp Bounds on the Distribution of a Function of Dependent Risks”. Journal of Computational and Applied Maths 236, 1833–1840] and Embrechts, Puccetti, and Rüschendorf [2013. “Model Uncertainty and VaR Aggregation”. Journal of Banking and Finance 37, 2750–2764] propose the rearrangement algorithm (RA) as a general method to approximate VaR bounds when the loss distributions of the different loans are known but not their interdependence (unconstrained bounds). Their numerical results show that the gap between worst-case and best-case VaR is typically very high, a feature that can only be explained by lack of using dependence information. We propose a modification of the RA that makes it possible to approximate sharp VaR bounds when besides the marginal distributions also higher order moments of the aggregate portfolio such as variance and skewness are available as sources of dependence information. A numerical study shows that the use of moment information makes it possible to significantly improve the (unconstrained) VaR bounds. However, VaR assessments of credit portfolios that are performed at high confidence levels (as it is the case in Solvency II and Basel III) remain subject to significant model uncertainty and are not robust.