Multivariate Spectral Backtests of Forecast Distributions under Unknown Dependencies

Janine Balter and Alexander J. McNeil ()
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Janine Balter: Deutsche Bundesbank, 40212 Düsseldorf, Germany
Alexander J. McNeil: School for Business and Society, University of York, York YO10 5DD, UK

Risks, 2024, vol. 12, issue 1, 1-15

Abstract: Under the revised market risk framework of the Basel Committee on Banking Supervision, the model validation regime for internal models now requires that models capture the tail risk in profit-and-loss (P&L) distributions at the trading desk level. We develop multi-desk backtests, which simultaneously test all trading desk models and which exploit all the information available in the presence of an unknown correlation structure between desks. We propose a multi-desk extension of the spectral test of Gordy and McNeil, which allows the evaluation of a model at more than one confidence level and contains a multi-desk value-at-risk (VaR) backtest as a special case. The spectral tests make use of realised probability integral transform values based on estimated P&L distributions for each desk and are more informative and more powerful than simpler tests based on VaR violation indicators. The new backtests are easy to implement with a reasonable running time; in a series of simulation studies, we show that they have good size and power properties.

Keywords: backtesting; risk management; value-at-risk; model validation; Basel regulations (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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