Interest rate risk: dimension reduction in the Swiss Solvency Test

Many risk models suffer from the incorporation of too many risk dimensions, which at best only increase computational costs. However, in many cases such models suffer in addition from a poor predictive power, as either the numerous underlying parameters are not understood fully and in order to remain computable the models may be over-simplistic and therefore neglect the more subtle interactions between the main risk drivers. In this paper, we analyze the interest rate risk module of the Swiss Solvency Test Standard Model, where interest rate risk is modeled with 13 risk-factors per currency. We apply the principal component analysis to reduce the dimension of this module. The economic interpretation of the remaining risk-factors becomes obvious, improving the understanding of the model. Further, we suggest to calculate the risk-factor sensitivities at the quantile corresponding to the expected shortfall of the corresponding normally distributed risk-factor. This way the inherent non-linearities are sufficiently allowed for and a complex second order Delta–Gamma approximation could be omitted. A sample calculation based on the SST 2011 for Basler Leben AG is provided to illustrate the validity of our approach with a real world case study.