A bridge between local GAAP and Solvency II frameworks to quantify capital requirement for demographic risk

The aim of this paper is to provide a stochastic model useful for assessing the capital requirement for demographic risk in a framework coherent with the Solvency II Directive. The model extends to the market consistent context classical methodologies developed in a local accounting framework. The random variable demographic profit, defined in literatue under local accounting principles, is indeed analysed in a Solvency II framework. We provide a unique formulation for different non-participating life insurance contracts and we prove analytically that the valuation of demographic profit can be significantly affected by the financial conditions in the market. Regarding this topic, we implement the Vašíček model to add randomness to risk-free rates. A case study has also been developed considering a portfolio of life insurance contracts. Results prove the effectiveness of the model in highlighting the main drivers of capital requirement evaluation (e.g., the volatility of both mortality rates and risk-free rates), also compared to the local GAAP framework.