Abstract
This paper captures and measures the longevity risk generated by an annuity product. The longevity risk is materialized by the uncertain level of the future liability compared to the initially foretasted or expected value. Herein we compute the solvency capital (SC) of an insurer selling such a product within a single risk setting for three different life annuity products. Within the Solvency II framework, we capture the mortality of policyholders by the mean of the Hull–White model. Using the numerical analysis, we identify the product that requires the most SC from an insurer and the most profitable product for a shareholder. For policyholders we identify the cheapest product by computing the premiums and the most profitable product by computing the benefit levels. We further study how sensitive the SC is with respect to some significant parameters.
Highlights
During the past decade, pension funds and insurers have faced numerous problems as consequences of the continuous increase of population life expectancy commonly called longevity risk
From the insurer’s viewpoint, the comparison is made using the level of the solvency capital (SC) of each different annuity and the internal rate of return on the SC invested by shareholders
We found that when the short rate increases, the SC decreases and the convex form obtained for the deferred annuity implies that there exists a computational time and a deferred period that minimizes the SC of the insurer
Summary
Pension funds and insurers have faced numerous problems as consequences of the continuous increase of population life expectancy commonly called longevity risk. Due to the longevity risk, insurers were obliged to increase the annuity prices in order to be more confident with regard to their solvency towards the policyholders. The particularities of the SII framework are based on its risk-sensitivity and its multi-risk factors; the latter means it recognizes that insurers face different kinds of risks, such as the equity, the longevity and the interest rate risks. In this regard, insurers have to focus on the computation of the so called solvency capital (SC) as defined in the SII regulation. We refer to the amount the insurance company or the insurer has to put aside in order to be solvent until the end of the contract in accordance with the SII regulation
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