Dynamic backtesting of value-at-risk models under regime change

Victor H. de la Pena, Ricardo Rivera

Abstract

ABSTRACT

The dislocation of the financial markets during the third quarter of 2007 caused an unusual number of exceptions in banks’ value-at-risk (VaR) models. In presence of regime change, the standard VaR backtesting method is inappropriate to assess the accuracy of the model. This paper introduces a dynamic (multi-period) method for backtesting models. The method is used to sequentially validate the VaR model for consecutive time periods (moving window samples). Banks’ risk managers tend to think about the large number of exceptions as a temporary phenomenon and assume that the model is fundamentally correct. Consequently, they do not incorporate the new data into the decision-making process. In contrast, our method fully uses the data to estimate the probability of an exception and to test whether or not the observed number of exceptions is consistent with the VaR backtesting assumptions. Under given conditions, we find that the acceptance or rejection of the model is a function of the number of exceptions that occurred in the current and past time periods. The dynamic backtesting approach is used to detect the emergence of a regime shift that can alert risk managers to revise the model. It also provides a way to estimate the VaR model risk under stress conditions. We show how the current Basel backtesting procedure can be modified to incorporate our approach. The dynamic approach can be extended to validate other risk management and pricing models.