Model Risk in the Fundamental Review of the Trading Book: The Case of the Default Risk Charge

The recent Fundamental Review of the Trading Book (FRTB) resulted in revised standards for capital requirements for market risks in a bank’s trading book. As part of the ruleset, default risk needs to be measured and capitalized through a dedicated Default Risk Charge (DRC). With the DRC as an extreme tail risk measure at 99.9% confidence level for portfolio default losses at a one-year horizon, there is inherent model risk associated with the reflection of joint defaults. Wilkens and Predescu (2017) proposed an overall framework for modeling the DRC that is based on a Gaussian factor copula model to capture the coincidence of defaults. This paper assesses the resulting model risk by analyzing alternative copulas (Gaussian, Student t, and Clayton) and the influence on the DRC figures with the help of a set of example portfolios. The copula choice can affect the DRC considerably, especially for directional and less diversified portfolios; the influence on typical larger-scale, diversified portfolios is much less pronounced. The uncertainty arising from the calibration of any copula from only a few data points – as implied by the regulation – is at least of equal importance as the selection of the dependence model itself.