Computing the Solvency Capital Requirement with Linear Regression and Neural Networks

Calculating the solvency II capital requirement when an insurance company uses an internal model is a tremendous task, especially as the corresponding EU directive requires to derive the solvency capital from the forecast of the full loss distribution function.

In this talk, we introduce the Least-Squares-Monte-Carlo-Approach for calculating the solvency capital. This approach is based on simulating the evolution of the relevant risk factors of the internal cash-flow-projection model to the end of the year and then in a market consistent way until the end of the projection horizon. By introducing a regression approach the calculation of the required runs of the cash-flow-projection model can be kept on a level such that the method remains computationally feasible.

We present two such regression approaches, a linear regression and a nonlinear regression method in the form of a feedforward neural network. Various aspects related to the calibration of the regression functions, their validation and their final use (including the presentation and analysis of the results) are explained by an application to data that are close to those of a German life insurer.