Techniques for Verifying the Accuracy of Risk Management Models

Risk exposures are typically quantified in terms of a "Value at Risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss probability distribution. Given their function both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to quantify the accuracy of an institution's VaR estimates. This study shows that the formal statistical procedures that would typically be used in performance-based VaR verification tests require large samples to produce a reliable assessment of a model's accuracy in predicting the size and likelihood of very low probability events. Verification test statistics based on historical trading profits and losses have very poor power in small samples, so it does not appear possible for a bank or its supervisor to verify the accuracy of a VaR estimate unless many years of performance data are available. Historical simulation-based verification test statistics also require long samples to generate accurate results: Estimates of 0.01 critical values exhibit substantial errors even in samples as large as ten years of daily data.

Kupiec P. (1995) Techniques for Verifying the Accuracy of Risk Management Models. Journal of Derivatives, 3, 73-84.