Backtesting Value-at-Risk: An Alternative Methodology*

By Giuseppe Arbia (Università Cattolica), Rong Chen (Rutgers), Giuseppe Corvasce, and Ruey Tsay (University of Chicago)

The paper proposes a novel statistical methodology for backtesting Value-at-Risk (VaR) models. The technique relies on the Ljung-Box test for the size of the hits, computed as the distance between the observed returns and the one step ahead forecasted VaR, when a violation occurs. The test determines whether or not the size of the hits are independent and identically distributed; whether or not the model shows lack of fit. The empirical analysis is applied to the S&P500 index, considering the levels of the VaR at 95% and 99%.

Contact Prof. Dr. Giuseppe Corvasce with questions about implementation.