Model risk in VaR estimation: An empirical study

Abstract

This paper studies the model risk; the risk of selecting a model for estimating the Value-at-Risk (VaR). By considering four GARCH-type volatility processes exponentially weighted moving average (EWMA), generalized autoregressive conditional heteroskedasticity (GARCH), exponential GARCH (EGARCH), and fractionally integrated GARCH (FIGARCH), we evaluate the performance of the estimated VaRs using statistical tests including the Kupiec's likelihood ratio (LR) test, the Christoffersen's LR test, the CHI (Christoffersen, Hahn, and Inoue) specification test, and the CHI nonnested test. The empirical study based on Shanghai Stock Exchange A Share Index indicates that both EGARCH and FIGARCH models perform much better than the other two in VaR computation and that the two CHI tests are more suitable for analyzing model risk. © World Scientific Publishing Company.