Evaluation of Various Approaches to Value at Risk

In the light of the current financial crisis, risk management and prediction of market losses seem to play a crucial role in finance. This thesis compares one day out-of-sample predictive performance of standard methods and conditional autoregressive VaR (CAViaR) by Engle & Manganelli (2004) for VaR (Value-at-risk) prediction of market losses. Comparison is made on US, Hong Kong, and Russian indices under tranquil period and current crisis using more than 10 years of daily returns. Performance is evaluated in terms of empirical coverage probability and predictive quantile loss on adequate models pointed out by Christoffersen test. The findings show that traditional methods such as historical simulation, normal VaR and t-VaR behave quite well in tranquil period if accounted for the return volatility dynamics by using GARCH volatility estimates. When unfiltered, these models fail to produce reliable results. In crisis period symmetric and asymmetric specifications of CAViaR showed good results, generally better and more stable than traditional approaches. Overall, CAViaR was found to work better on 5% than on 1% level. However, this model class is in most cases outperformed by conventional filtered models in the tranquil period. Little evidence was found that the market type has impact on the choice of ideal VaR model