Testing of models utilized for VaR estimation

Abstract

Modeling, measuring, and subsequent management of the portfolio risks is of great importance for decision making in financial institutions. This article is focused on the portfolio returns modeling with the use of two particular probability distributions, normal distribution and normal inverse Gaussian model. The normal distribution is chosen because of its general and easy use and normal inverse Gaussian distribution is selected because of its ability to model the skewness and kurtosis. The goals of the article are to backtest chosen models for VaR estimation and to choose the best one. Models based on these two distributions are compared on the basis of VaR estimation of market risk. The backtesting results are statistically tested on the number and independence of the exceptions. The conclusion, that the models which utilize the normal inverse Gaussian model are for portfolio modeling more appropriate than those with normal probability distribution, is based on the results shown in the application part of the article. On the other hand even these models are not accurate for VaR estimation on lower confidence levels because of the existence of bunching.