Assessing the Model Risk with Respect to the Interest Rate Term Structure Under Solvency II

Abstract

Interest rate risk, i.e. the risk of changes in the interest rate term structure, is of high relevance in insurers’ risk management. Due to large capital investments in interest rate sensitive assets such as bonds, interest rate risk plays a considerable role for deriving the solvency capital requirement (SCR) in the context of Solvency II. In addition to the Solvency II standard model, we apply the model of Gatzert and Martin (2012) for introducing a partial internal model for the market risk of bond exposures. The aim of this paper is to assess model risk with focus on bonds in the market risk module of Solvency II regarding the underlying interest rate process and input parameters. After introducing calibration methods for short rate models, we quantify interest rate and credit risk for corporate and government bonds and demonstrate that the type of process can have a considerable impact despite comparable underlying input data. The results show that, in general, the SCR for interest rate risk derived from the standard model of Solvency II tends to the SCR achieved by the short rate model from Vasicek (1977), while the application of the Cox, Ingersoll, and Ross (1985) model leads to a lower SCR. For low-rated bonds, the internal models approximate each other and, moreover, show a considerable underestimation of credit risk in the Solvency II model.