Measuring profitability of life insurance products under Solvency II

In this paper, we propose an enhanced method for the measurement of profitability of life insurance products. In contrast to most of the existing literature, we consider the development of the insurance contracts over their entire lifetime under the real-world probability measure and distinguish between different sources of capital. We study the pathwise realization of random variables describing shareholder profitability to obtain and analyze their distribution. These distributions are more versatile than single statistics such as expected values since they additionally allow for the analysis of extreme outcomes. Moreover, we specifically consider the strain on shareholders arising from the solvency capital requirement under Solvency II. We use a cost of capital approach based on the explicit computation of the solvency capital requirement and the interrelated capital required from shareholders for each year of the projection period. To demonstrate the feasibility of our profit measures, we provide a concrete application to products with interest rate guarantees including an internal model approach for market risks under Solvency II. Our numerical application shows that our proposed profit measures are particularly suitable for revealing the profitability of different life insurance products in today's regulatory environment.