Comparison of Value at Risk, Expected Shortfall, and Range Value at Risk with numerical examples

Abstract

This thesis intends to examine three risk measures - Value at Risk (VaR), Expected Shortfall (ES) and Range Value at Risk (RVaR), used to forecast probable future losses. The first part of the thesis gives an overview - the definition, formulas, and advantages and disadvantages - of these three risk measures. In the second part of the thesis, the estimation of the risk measures will be implemented using Monte Carlo simulation and their application in insurance companies when building non-life models. We analyse the errors from our estimation and finally examine the sensitivity due to changes in each parameter ceteris paribus.