Ein zweidimensionales Durationskonzept

The German proposal for a Solvency II-compatible standard model for the life insurance branch calculates the risk capital that is necessary for a sufficient risk capitalisation of the company at hand. This capital is called ‘‘target capital’’ or Solvency Capital Requirement (SCR for short). For this to achieve it is applied the book value of the actuarial reserve onto the well-known market value formula getting the market value (or present value) by means of the classical duration concept as a global approach (cf. the documentation of the standard model of the GDV p. 26). This formula takes into account the impact of the interest rate but leaves aside all the other actuarial assumptions. In particular, the influence of the biometrical assumptions is not considered. This is at least one reason, why this ansatz is – at the time being – no more compatible with the Solvency II requirements and thus does no more satisfy its own entitlements. In the work at hand it is proposed and worked out a concept that overcomes this drawback. The result is a formula with the help of which the present value of the actuarial liabilities is calculated from their book value in fact by taking into account the interest rate as well as the biometrical assumptions. It is to be remarked that the proposed two-dimensional duration concept may be developed completely along the lines given by the classical one-dimensional analogue leaving some arbitraries only on determining the biometrical gauge, i.e., the mapping of the vector that represents the formula of the active lives remaining onto its average value. For this to achieve one has to consider the underlying business in force. The superordinate relevance of such a two-dimensional ansatz lies in the fact that the developments of the project Solvency II during the last months have shown that its success depends crucially on the availability of efficient and well-elaborated approximation procedures.