The New International Regulation of Market Risk: Roles of VaR and CVaR in Model Validation

Abstract

We model the new quantitative aspects of market risk management for banks that Basel established in 2016 and came into effect in January 2019. Market risk is measured by Conditional Value at Risk (CVaR) or Expected Shortfall at a confidence level of 97.5%. The regulatory backtest remains largely based on 99% VaR. As additional statistical procedures, in line with the Basel recommendations, supplementary VaR and CVaR backtests must be performed at different confidence levels. We apply these tests to various parametric distributions and use non-parametric measures of CVaR, including CVaR- and CVaR+ to supplement the modelling validation. Our data relate to a period of extreme market turbulence. After testing eight parametric distributions with these data, we find that the information obtained on their empirical performance is closely tied to the backtesting conclusions regarding the competing models.

Keywords: Basel III, VaR, CVaR, Expected Shortfall, Back-Testing, Parametric Model, Non-Parametric Model, Mixture of Distributions, Fat-Tail Distribution

JEL Classification: C44, C46, C52, G21, G24, G28, G32