Regulatory Evaluation of Value-at-Risk Models

Value-at-risk (VaR) models have been accepted by banking regulators as tools for setting capital requirements for market risk exposure. Three statistical methodologies for evaluating the accuracy of such models are examined; specifically, evaluation based on the binomial distribution, interval forecast evaluation as proposed by Christoffersen (1995), and distribution forecast evaluation as proposed by Crnkovic and Drachman (1995). These methodologies test whether the VaR forecasts in question exhibit properties characteristic of accurate VaR forecasts. However, the statistical tests used often have low power against alternative models. A new evaluation methodology, based on the probability forecasting framework discussed by Lopez (1995), is proposed. This methodology gauges the accuracy of VaR models using forecast evaluation techniques. It is argued that this methodology provides users, such as regulatory agencies, with greater flexibility to tailor the evaluations to their particular interests by defining the appropriate loss function. Simulation results indicate that this methodology is clearly capable of differentiating among accurate and alternative VaR models. This paper was presented at the Financial Institutions Center's October 1996 conference on "