Abstract

Value at Risk Approaches in the Case of Fat-Tailed Distributions of Risk Factors

Gabriela de Raaij and Burkhard Raunig

Austrian National Bank

We analyze variance-covariance methods, historical simulation approaches and a new method based on mixtures of normal distributions when the distributions of risk factors have fat tails. Daily VaR numbers are estimated for twenty randomly chosen foreign exchange portfolios over a period of one thousand trading days. Although the same parameters (confidence level, holding period) are used for all models, our results indicate that comparisons of VaR-numbers generated by different models can be misleading. We also analyze how accurately the VaR-estimates of the models match the specified confidence intervals. For our portfolios the new methodology performs best.