A Bridge between Local GAAP and Solvency II Frameworks to Quantify Capital Requirement for Demographic Risk

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.

A stochastic model for capital requirement assessment for mortality and longevity risk, focusing on idiosyncratic and trend components

“…We recall the definition of the random variable (r.v.) demographic profit ỹMCV t+1 1 (see Clemente et al, 2021) for the decomposition of the whole insurance profit in a market consistent context according to the framework defined by the Solvency II directive (see European Parliament andCouncil, 2009 andEuropean Parliament andCouncil, 2014)…”

“…Although this paper is not related to a market-consistent valuation (MCV), it models the single generations of the insurance portfolio with an exact individual approach. Clemente et al (2021) describe the bridge between Local GAAP and Solvency II contexts, highlighting the effects of the market-consistent assessment of liabilities on the random variable (r.v.) demographic profit.…”

A Discrete Risk-Theory Approach to Manage Equity-Linked Policies in an Incomplete Market

“…These bases are P * and j * , respectively, first-order demographic base (prudential) and first-order financial base, also called the technical rate. In other words, the insurance company uses probabilities greater than those considered realistic (second-order demographic basis) and a technical rate lower than the return it expects to obtain from investments on the market to have a positive expected profit (for further comments, see Clemente et al (2021)). Consistent with the above, it is possible to define the Fair Premium (FP) of the policy (not charged by the insurer as it lacks safety loading) as…”

Special Issue “Quantitative Risk Assessment in Life, Health and Pension Insurance”

“…(i) Design of new pension insurance products and risk-management of loan insurance (Olivieri 2021;Planchet et al 2022); (ii) Assessing capital requirements for demographic risk in a life insurance portfoliostochastic models and numerical techniques (Clemente et al 2021;Costabile and Viviano 2021); (iii) Analysis and risk-management of the long-term impact of COVID-19 on the life insurance business (Carannante et al 2022).…”

“…In detail, the paper by (Clemente et al 2021) focuses on the evaluation of capital requirements for both mortality and longevity risk. To this end, a stochastic model for traditional life insurance contracts is proposed and framed within the Solvency II Directive.…”