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Encyclopedia of Financial Models, 3 Volume Set by Frank J. Fabozzi

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Back-Testing Market Risk Models

KEVIN DOWD, PhD

Partner, Cobden Partners, London

Abstract: Back-testing is the quantitative evaluation of a model, and back-testing a risk or probability density forecasting model involves a comparison of the model's density forecasts against subsequently realized outcomes of the random variable whose density is forecast. One purpose of back-testing is to determine whether the forecasts are sufficiently close to realized outcomes to enable us to conclude that the forecasts are statistically compatible with those outcomes. Back-tests conducted for this purpose involve statistical hypothesis tests to determine if a model's forecasts are acceptable. Hypothesis tests can be applied to observations involving a loss that exceeds the value-at-risk at a given confidence interval, or they can be applied to forecasts of VaRs at multiple confidence intervals. A second purpose of back-testing is to assist risk managers to diagnose problems with their risk models and so help improve them. A third purpose of back-testing is to rank the performance of a set of alternative risk models to determine which model gives the “best” density forecast evaluation performance.

To back-test a model is to evaluate it in quantitative terms, and back-testing a risk (or probability density forecasting) model involves a comparison of the model's density forecasts against subsequently realized outcomes of the underlying random variable whose density is forecast. The importance ...

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