英文标题：
《There is a VaR beyond usual approximations》
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作者：
Marie Kratz
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最新提交年份：
2013
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英文摘要：
Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the use of the Central Limit Theorem (CLT), when assuming aggregation of independent and identically distributed (iid) observations in the portfolio model. Such a choice of modeling, in particular using light tail distributions, has proven during the crisis of 2008/2009 to be an inadequate approximation when dealing with the presence of extreme returns; as a consequence, it leads to a gross underestimation of the risks. The main objective of our study is to obtain the most accurate evaluations of the aggregated risks distribution and risk measures when working on financial or insurance data under the presence of heavy tail and to provide practical solutions for accurately estimating high quantiles of aggregated risks. We explore a new method, called Normex, to handle this problem numerically as well as theoretically, based on properties of upper order statistics. Normex provides accurate results, only weakly dependent upon the sample size and the tail index. We compare it with existing methods.
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中文摘要：
Basel II和Solvency 2都使用风险价值（VaR）作为计算资本要求的风险度量。在实践中，为了校准VaR，通常会对金融资产年对数收益率的未知分布选择正态近似值。当假设投资组合模型中独立同分布（iid）观测值的集合时，这通常通过使用中心极限定理（CLT）来证明。在2008/2009年的危机期间，这种建模选择，尤其是使用轻尾分布，已经证明在处理极端回报的存在时是不够的近似；因此，它导致对风险的严重低估。我们研究的主要目标是在存在重尾的情况下处理金融或保险数据时，获得对聚合风险分布和风险度量的最准确评估，并为准确估计聚合风险的高分位数提供实际解决方案。基于高阶统计量的性质，我们探索了一种新的方法，称为Normex，从数值和理论上处理这个问题。Normex提供了准确的结果，仅弱依赖于样本量和尾部指数。我们将其与现有方法进行了比较。
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分类信息：

一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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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