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 regarding the capital requirements for market risks in a bank’s trading book. As part of the rule set, default risk needs to be measured and capitalized through a dedicated Default Risk Charge (DRC). With the DRC being an extreme tail risk measure at a 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. In 2017, Wilkens and Predescu proposed an overall framework for modeling the DRC, 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 their influence on DRC figures with the help of a set of example portfolios. The copula choice can affect the DRC considerably, especially for less diversified, directional portfolios. The influence on typical larger-scale, diversified portfolios is much less pronounced. The uncertainty arising from the calibration of any copula using only a few data points – as implied by the regulation – is of at least equal importance as the selection of the dependence model itself.