Calacualting Value at Risk and Expected Shortfall of Some Statistical Distributions

Value at risk and expected shortfall are the two most popular measures for calculating financial risk.
To calculate these measures (Value at risk and expected shortfall) there are many approaches, which can be divided into two main categories; parametric and non-parametric. In parametric approach it is supposed that the distribution of asset return belongs to a specific class of distributions. For some distributions we can claculate easily the mentioned measures. In this paper the the relation of epected shortfall has been proved for four symetric distribution.