Exponential Autoregressive Conditional Duration Approach to Testing VaR

Abstract

As laid out by the current Basel III accord and the Basel IV agreements, financial risk model evaluation remains based on the VaR measure. However, existing VaR backtesting methods are repeatedly criticized due to unsatisfactory power properties. Our contribution to the debate is the exploration of the properties of the exponential autoregressive conditional duration (EACD) model in the context of backtesting VaR. We show that the EACD test, although exhibiting strong power, suffers from size distortions when the true parameter is near or at the boundary of the parameter space. To remedy this problem we suggest asymptotic p-value computation with the use of the mixture of the chi square distributions. We obtain a procedure that is both accurate and computationally effective. We show that it has the potential to improve effectiveness of detecting incorrect risk models.