Analytical solution of Value at Risk and Expected Shortfall conditioned by mixture normal distribution

作者:Valecky Jiri; Kresta Ales
来源:5th International Scientific Conference on Managing and Modelling of Financial Risk, 2010-09-08 to 2010-09-09.

摘要

Analytical solution of Value at Risk and Expected Shortfall conditioned by mixture normal distribution
The assumption of normal probability distribution belongs to the biggest imperfections of analytical solution of Value at Risk and Expected Shortfall. However, the returns are rather distributed leptokurtic and the empirical distributions are often skewed. In these cases, this assumption results in over- or underestimation of VaR and ES compared with the genuine values. This paper is devoted to analytical solution of VaR and ES under the assumption of normal mixture probability distribution by which it is possible to characterize the typical leptokurtic distribution of financial assets' return. Firstly, the analytical solution of VaR and ES under normal distribution and under normal mixture distribution condition is described. Next, the techniques of estimating parameters of probability distributions are presented, i.e. general method of moments and maximum likelihood. Finally, the particular Value at Risk and Expected Shortfall are calculated and the results are compared.

  • 出版日期2010