Industry standard and econometric standard: the search for powerful approach to evaluate var models

Abstract

Under the Basel III and Basel IV accords, risk model validation remains based on the VaR measure. According to the industry practice, VaR backtesting procedures rely on two likelihood ratio tests, which, in light of the academic research, have been criticized for their unsatisfactory power. This paper aims to show the differences between VaR model evaluation based on the standard likelihood ratio approach and backtesting by means of other econometric methods applicable to the binary VaR failure process. The author decomposed the model evaluation into testing the unconditional coverage, replaced the likelihood ratio with a normal statistic, and in the next stage in order to verify the conditional coverage, employed the Ljung-Box statistic. The study experimentally confirmed the superiority of the proposed procedures over the industry standards. The main contribution, however, is the empirical study designed to demonstrate the practical differences in risk analysis attributable to the choice of the backtesting method. Using data on leading stock market indexes, from various periods, the author showed that the practical conclusions from backtesting diverge markedly due to the test choice. The proposed, more powerful tests, contrary to the standard procedures, allowed for distinguishing distinct models of index behaviour connected with undergoing the financial crises.