Value at Risk Estimation A GARCH-EVT-Copula Approach
Value at Risk Estimation A GARCH-EVT-Copula Approach
复制标题
风险价值估计 GARCH-EVT-Copula 方法
DOI：
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发表时间：
2013
期刊：
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通讯作者：
Ngoga Kirabo Bob
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文献类型：
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作者：
Ngoga Kirabo Bob
风险价值(Value at Risk，VaR)是风险管理中应用最广泛的风险度量之一。它被定义为在给定的置信度水平下，在给定的时间范围内，投资组合可预期的最大损失。在本文中，我们使用一种结合Copula函数、极值理论和GARCH模型的方法来估计投资组合的VaR。我们将这种方法应用于由德国、西班牙、意大利和法国的股票指数组成的投资组合。为了估计这一投资组合的VaR，我们首先使用非对称GARCH模型和EVT方法对每个对数收益序列的边际分布进行建模，然后使用Copula函数(高斯、学生t、Clayton、Gumbel和Frank)将边际分布连接成一个多元分布。然后，我们使用蒙特卡罗模拟(MCS)方法来寻找投资组合VaR的估计。为了检查该方法的拟合优度，我们使用了回溯测试方法。结果表明，总体上，GARCH-EVT-Copula方法表现良好，特别是GARCH-EVT-Student‘s t Copula方法优于所有其他GARCH-EVT-Copula方法和传统方法，如历史模拟(HS)和方差协方差
Value at Risk (VaR) is one of the most widely used risk measure in risk management. It is defined as the worst loss to be expected of a portfolio over a given time horizon at a given confidence level. In this thesis we estimate portfolio VaR using an approach combining Copula functions, Extreme Value Theory (EVT) and GARCH models. We apply this approach to a portfolio consisting of stock indices from Germany, Spain, Italy and France. To estimate the VaR of this portfolio, we first use an asymmetric GARCH model and an EVT method to model the marginal distributions of each log returns series and then use Copula functions (Gaussian, Student’s t, Clayton, Gumbel and Frank) to link the marginal distributions together into a multivariate distribution. We then use Monte Carlo Simulation (MCS) approach to find estimates of the portfolio VaR. To check the goodness of fit of the approach we use Backtesting methods. From the results, we conclude that, in general the GARCH-EVT-Copula approach performs well and specifically the GARCH-EVT-Student’s t Copula outperforms all other GARCH-EVT-Copulas and traditional methods such as Historical Simulation (HS) and Variance Covariance