Multivariate Spectral Backtests of Forecast Distributions under Unknown Dependencies

TY - JOUR

T1 - Multivariate Spectral Backtests of Forecast Distributions under Unknown Dependencies

AU - Balter, Janine

AU - McNeil, Alexander John

N1 - © 2024 by the authors

PY - 2024/1/17

Y1 - 2024/1/17

N2 - 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.

AB - 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.

U2 - 10.3390/risks12010013

DO - 10.3390/risks12010013

M3 - Article

SN - 2227-9091

VL - 12

JO - Risks

JF - Risks

IS - 1

M1 - 13

ER -