Parametric Estimation of Value at Risk

Abstract: Previous research has shown that the non-parametric Value at Risk methods normally used by financial institutions are conservative and that violations often happen in clusters. While earlier research has found efficiency gains from using parametric methods over non-parametric methods, a majority of the studies have been carried out on equity indices. Parametric modelling of variance requires underlying distributional assumptions that depend on return characteristics. This thesis evaluates the use of parametric Value at Risk methods for different asset classes. The empirical analysis tests six different parametric methods; a standard variance model, RiskMetrics, a normal symmetric GARCH, a normal asymmetric GARCH, a symmetric t-distributed GARCH and an asymmetric t-distributed GARCH on 17 different assets. The data consists of daily indices and exchange rates from 2000 to 2013. The models are backtested by Christoffersen's (1998) conditional coverage test and by the backtest from the Basel Committee on Banking Supervision that determines market risk capital requirements from Value at Risk estimates. The results show that asset classes matter for the choice of parametric method. While an asymmetric t-distributed GARCH fulfils the criterion of conditional coverage for equity, different parametric models work well for different assets. One implication from this is that earlier research on equity cannot be generalized. The analysis also tests the models on an equally weighted portfolio of all assets and finds that parametric methods in general work well for a well-diversified portfolio. The results also show that there is a tension between the most accurate model and the model giving the lowest capital charge.