DP3403 An Evaluation Framework for Alternative VaR Models

Author(s): Dennis Bams, Thorsten Lehnert, Christian C Wolff
Publication Date: June 2002
Keyword(s): estimation risk, exchange rate positions, fat tail distributions, financial time series, GARCH, value-at-risk
JEL(s): C22, C52, G10
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=3403

In this Paper we investigate the ability of different models to produce useful VaR-estimates for exchange rate positions. We make a distinction between models that include sophisticated tail properties and models that do not. The former type of models often leads to too extreme VaR-estimates, whereas the latter type underestimates the risk in case of extreme events. Our analysis shows that it is important to take into account parameter uncertainty, since this leads to uncertainty in the reported VaR. We make this uncertainty in the VaR explicit by means of simulation. Our empirical results suggest that more sophisticated tail-modeling approaches come at the cost of more uncertainty about the VaR estimate itself. In the case of the GARCH(1,1)-Student-t model the average VaR may be adjusted for parameter uncertainty to arrive at levels which are adequate according to out-of-sample tests.