基于ARMA-GARCH模型的风险价值与条件风险价值计算

A Calculation of VaR and CVaR Based on ARMA-GARCH Model

关键词:  风险度量  风险价值  条件风险价值  GARCH模型

Key words:  risk measurement  VaR  CVaR  GARCH model

摘要:

基于ARMA-GARCH模型,给出风险价值VaR、条件风险价值CVaR的计算公式,分别在标准正态分布、student'T分布、Skewed-T分布、广义误差分布条件下对模型进行数值模拟,并用上证A股、大同煤业股票相关数据拟合模型来进行实证分析.结果表明,利用ARMA-GARCH模型给出的计算公式能够准确地估计VaR值与CVaR值,并且随着给定概率水平p的减少,VaR与CVaR的值增大,对于给定同一概率水平的CVaR值比VaR值大,CVaR比VaR更能体现风险度量的大小.

Abstract:

Based on ARMA-GARCH model, the formula for calculating the risk of the value of VaR and the value at risk conditions of CVaR are given, respectively, in the standard normal distribution, student'T distribution, Skewed-T distribution, the generalized error distribution model under the condition of numerical simulation. Simulation results show that the use of ARMA-GARCH model can more accurately estimate VaR and CVaR.At last we use Shanghai Stock Index and Datong Coal stock close of empirical data analysis, results showed that with a given probability level p reduction, VaR and CVaR values increase;the same probability for a given level, the value of CVaR are bigger than that of VaR, so CVaR risk measure is better than VaR.