Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 9. Back-Testing Market Risk Models

KEVIN DOWD, PhD

Professor of Financial Risk Management, Centre for Risk and Insurance Studies, Nottingham University Business School

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 backtesting 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. Backtests 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 backtesting is to assist risk managers to diagnose problems with their risk models and so help improve them. A third purpose of backtesting is to rank the performance of a set of alternative risk models to determine which model gives the "best" density forecast evaluation performance.

Keywords: back-testing, market risk models, value at risk, binomial distribution, conditional testing approach, runs test, Christoffersen approach, probability integral transformation, Berkowitz transformation, testing ...