Abstract
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.
Highlights
Introduction to Quantify Capital Requirement forTwo key innovations, brought by the Solvency II directive in insurance, are the introduction of the market consistent framework for the valuation of assets and liabilities and the definition of risk-based principles for the assessment of the Capital Requirement.In this context, the quantification of losses on an annual time horizon at a given confidence level is a crucial element in determining the requirement
We focus on the evaluation of the capital requirements for both mortality and longevity risk
We adapt classical actuarial relations to the market consistent framework required by the Solvency II directive
Summary
Brought by the Solvency II directive in insurance, are the introduction of the market consistent framework for the valuation of assets and liabilities and the definition of risk-based principles for the assessment of the Capital Requirement. Several sources of risk are involved in the valuation process; measuring the dependence between them is a crucial point In this framework, we focus on demographic profit and we provide a stochastic model to quantify the capital requirement for both mortality and longevity risk. Further research will concern the aggregation of several cohorts and portfolios composed of different contracts in order to catch the effects of both dependencies and natural hedging (see, e.g., Cox and Lin 2007) Through this model, we prove the analytical decomposition of the expected demographic profit/loss, highlighting main drivers. Technical Provisions and the market consistent valuation of Solvency II Best Estimate, must consider the effect of risk-free rates component. The sum of these five components gives back the whole technical profit (see Equation (2))
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