Interest rate risk and the Swiss Solvency Test

Abstract

The Swiss Solvency Test (SST) encompasses the market-consistent valuation of claims and liabilities as well as risk-based capital coverage for insurers. It is, however, virtually impossible to conduct a market-consistent valuation of liabilities because market prices for insurance liabilities are extremely scarce in practice. For this reason, a market-consistent valuation is approximated by calculating the present value of insurance cash flows. The valuation of insurance liabilities therefore essentially depends on the spot interest rates used. As a further consequence, solvency capital backing is also based on the spot interest rates used. This paper examines how spot rates are modelled for the purpose of risk measurement under the SST standard model and identifies three shortcomings.First, the SST risk model is based on a large number of interest rate risk factors which necessitate extremely extensive calculation when making a stochastic risk measurement for insurance liabilities and are therefore difficult to compute within a useful timeframe. The SST envisages the modelling and numerical simulation of spot rates for 13 representative maturities for each currency. This is not just time-consuming but also unnecessarily complex.Second, with respect to risk measurement, the SST assumes normally distributed spot rate changes. This assumption can result in clearly negative and therefore implausible simulations of nominal spot rates, with a particularly serious impact within the currently prevailing low interest rate environment.Finally, the SST model typically tends toward pro-cyclical capital requirements when capturing interest rate risk. The assumption of normally distributed interest rate changes forces insurance entities to hold more capital in a low interest rate environment than in a high interest rate environment. In actual fact, however, the potential for losses arising from falling interest rates within a low interest rate environment is limited and for this reason higher capital requirements do not appear to make sense in economic terms.The model put forward by this paper aims to overcome the shortcomings relating to interest rate modelling that are entailed in the SST standard model. First, we use a systematic analysis of the yield curve for spot rates to show how the number of risk factors can be reduced. We propose moving away from individual interest rates for representative maturities, instead modelling the yield curve for all possible maturities directly. In particular, this serves to ensure that numerically simulated yield curves also display the usual empirical form and that the number of interest rate risk factors can be reduced to three per currency.In addition, it is assumed that spot rates are not normally distributed but instead exhibit a truncated normal distribution pattern, whereby the constraint on interest rate distribution is inferred from the existence of an interest rate lower bound. Such a restriction appears empirically and theoretically reasonable: first, no significant negative ...

Scenario-based measurement of interest rate risks

“…5. An alternative approach for incorporating lower bounds for interest rates has been proposed by Eder et al (2014). The authors include lower bounds by means of a plane-truncated normal distribution.…”