Testing VaR Under Basel III with Application to No-Failure Setting

We investigated practical aspects of VaR model testing in case of no-failure series, with the special focus on significance levels recommended under Basel III. We considered alternative approaches to the standard likelihood ratio (LR) statistics, which are Wald and Lagrange Multiplier (LM) tests. The aim of the paper was to propose a VaR test available directly for no-failure setting and to compare VaR tests based on various rules—LR, Wald and Lagrange Multiplier. The comparative analysis involved both practical applicability aspects and formal evaluation of statistical properties of the tests. We showed that the LM rule applied to VaR test construction offers a practical advantage of direct applicability to all kinds of observed failure sequences, independent on the number of VaR breaches. We also presented possible power gains, resulting from the alternative approach, which result in more effective detection of misspecified risk models.