Journal of Risk Model Validation

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Model risk in the Fundamental Review of the Trading Book: the case of the Default Risk Charge

Sascha Wilkens and Mirela Predescu

  • This paper assesses the model risk associated with the copula choice for the calculation of the Default Risk Charge (DRC) measure.
  • Alternative copulas (Gaussian, Student t, and Clayton) are explored and the influence on the DRC figures is analyzed with the help of a set of example portfolios.
  • It is found that 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 is at least of equal importance as the selection of the dependence model itself.

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.

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