Journal of Risk

The present issue of The Journal of Risk contains papers that address the impact of model risk on capital requirements, and also includes robust approximation approaches for risk assessment and risk attribution.

The first paper, "Model uncertainty in risk capital measurement" by Valeria Bignozzi and Andreas Tsanakas, introduces two new measures to assess model risk and parameter estimation risk, respectively. The authors then use these measures to show that, for nonparametric models, historical simulation understates capital requirements while the worst-case scenario overstates them. Through a numerical study they also show that the natural approach of averaging across parametric models does not confer an advantage to better estimate solvency capital.

In the second paper, "Basel II versus III: a comparative assessment of minimum capital requirements for internal model approaches", Harald Kinateder performs an analytical comparison of the three prominent versions of the Basel accords for the minimum capital requirement (MCR). He shows that the MCR under Basel II during a stress period is adequate only if the value-at-risk (VaR) upon which it is based accounts for significant kurtosis (ie, fat tails) and negative skewness. On the other hand, the MCR that results from the application of the 2010 version of Basel III is amply sufficient even with a poorly calibrated VaR. Furthermore, he finds that the MCR under the 2013 version of Basel III is only marginally higher than that of Basel II under the assumption of normal tails.

In "On optimal smoothing of density estimators obtained from orthogonal polynomial expansion methods", the third paper of this issue, Kohei Marumo and Rodney C. Wolff present a method that improves upon the approximation quality of the classical Hermite expansion of statistical distributions. Instead of the saddlepoint approach, theirs is based on standardization, smoothing and optimization, and requires only a finite expansion degree. Through numerical illustrations they demonstrate the effectiveness of their method for risk management evaluation in the context of both empirical and parameterized distributions.

While the previous paper focused on the application of Hermite polynomials to unidimensional distributions, in the fourth and final paper of this issue, "The application of Hermite polynomials to risk allocation", Francois Buet-Golfouse and Anthony W. Owen consider multivariate expansions under some restrictions. Their approach results in expressions with high-order adjustments for VaR as well as for expected shortfall (ES). It also provides an accurate and flexible method to determine risk attribution for both VaR and ES measures and is illustrated on a loan portfolio.

Farid AitSahlia
University of Florida