Regulatory Evaluation of Value-at-Risk Models

Abstract

Beginning in 1998, U.S. commercial banks may determine their regulatory capital requirements for financial market risk exposure using value-at-risk (VaR) models i.e., models of the time-varying distributions of portfolio returns. Currently, regulators have available three hypothesis-testing methods for evaluating the accuracy of VaR models: the binomial method, the interval forecast method and the distribution forecast method. These methods use hypothesis tests to examine whether the VaR forecasts in question exhibit properties characteristic of accurate VaR forecasts. However, given the low power often exhibited by these tests, these methods may often misclassify forecasts from inaccurate models as accurate. A new evaluation method that uses loss functions based on probability forecasts, is proposed. Simulation results indicate that this method is capable of differentiating between forecasts from accurate and inaccurate, alternative VaR models.

Keywords: value-at-risk, volatility modeling, probability forecasting, bank regulation

JEL Classification: C52, G2, G15