Value at Risk and Expected Shortfall under normal mixture distribution condition

被引:0
作者
Valecky, Jiri [1 ]
机构
[1] Tech Univ Ostrava, Fac Econ, Dept Finance, Sokolska 33, Ostrava 70121, Czech Republic
来源
PROCEEDINGS OF 47TH EWGFM MEETING | 2010年
关键词
Value at Risk; Expected Shortfall; mixture normal distribution; maximum likelihood; EM-algorithm; Monte Carlo simulation;
D O I
暂无
中图分类号
F [经济];
学科分类号
02 ;
摘要
The assumption of normal probability distribution belongs to the biggest imperfections of estimating Value at Risk and Expected Shortfall. In point of fact, the returns of financial time series are rather distributed leptokurtic than normally. Moreover, the empirical distributions are often skewed. In these cases, the assumption of normal distribution results in over- or underestimation of VaR and ES especially when the quantiles are very high/low. Therefore it is necessary to put emphasis on respecting the leptokurtic and skewed return distribution. In this paper, we interpret the one out of the method how to estimate VaR and ES with respect to the empirical distributions. We describe the analytical solution of VaR and ES under normal distribution and under normal mixture distribution condition and we compare the estimates according to both approaches. We also present the estimation method of distribution parameters. Thus, we briefly describe and derive the maximum likelihood method based on the iterative EM-algorithm. Using the four selected market portfolios (DAX, FTSE 100, PX and SP 500) we estimate the parametric and Monte Carlo VaR (ES respectively) and we give evidence that the estimates are very inaccurate when the normal distribution is assumed.
引用
收藏
页码:175 / 183
页数:9
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