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Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall

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JournalJournal of Banking and Finance
DateAccepted/In press - 8 Jan 2018
DateE-pub ahead of print (current) - 13 Jan 2018
Number of pages48
Early online date13/01/18
Original languageEnglish

Abstract

Under the Fundamental Review of the Trading Book, capital charges are based on the coherent Expected Shortfall (ES) risk measure, which is sensitive to tail risk. We argue that backtesting of the forecasting models used to derive ES can be based on a multinomial test of Value-at-Risk (VaR) exceptions at several levels. Using simulation experiments with heavy-tailed distributions and GARCH volatility models, we design a statistical procedure to show that at least four VaR levels are required to obtain tests for misspecified trading book models that are more powerful than single-level (or even two-level) binomial exception tests. A traffic-light system for model approval is proposed and illustrated with three real-data examples spanning the 2008 financial crisis.

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