Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II.

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

Longevity Risk and Reinsurance strategies for enhanced pensions

EnThis paper deals with demographic risk analysis in Enhanced Pensions, i.e. Long Term Care (LTC) insurance covers for retired. Both disability and longevity risk affect such a cover. Specifically, we concentrate on the risk of systematic deviations between projected and realised Specifically, we concentrate on the risk of systematic deviations between projected and realised mortality and disability, adopting a multiple scenarios approach. To this purpose we study the behaviour of the random risk reserve. Moreover, we analyse the effect of demographic risk on Risk-Based Capital requirements considering different time horizons and confidence levels and explaining how they can be reduced through either safety loading and reinsurance strategy. A profit analysis is also considered

Longevity risk and economic growth in sub-populations: evidence from Italy

Forecasting mortality is still a big challenge for Governments that are interested in reliable projections for defining their economic policy at local and national level. The accuracy of mortality forecasting is considered an important issue for longevity risk management. In the literature, many authors have analyzed the long-run relationship between mortality evolution and socioeconomic variables, such as economic growth, unemployment rate or educational level. This paper investigates the existence of a link between mortality and real gross domestic product per capita (GDPPC) over time in the Italian regions. Empirical evidence shows the presence of a relationship between mortality and the level of real GDPPC (and not its trend). Therefore, we propose a multi-population model including the level of real GDPPC and we compare it with the Boonen–Li model (Boonen and Li in Demography 54:1921–1946, 2017). The validity of the model is tested in the out-of-sample forecasting experiment

Frailty-based Lee–Carter family of stochastic mortality models

In the actuarial literature, frailty is defined to be the unobserved variable which encompasses all the factors affecting human mortality other than gender and age. Heterogeneity in individual frailty can play a significant role in population mortality dynamics. In the present paper, we identify the main latent factors that explain the frailty component, in order to clarify its role in mortality projections. We show, using longitudinal survey data, that frailty is mainly due to co-morbidities that impact on the process of deterioration in terms of the human body’s physiological capacity. Accordingly, we provide frailty-based stochastic models for projecting mortality based on the Lee–Carter family of models. We propose several versions that consider frailty both as an age-dependent and a time-dependent factor and also combining the interaction effects of age and time in comparison with the general level of mortality, and compare the resulting mortality projections using data from England

Longevity Risk and Reinsurance strategies for enhanced pensions

EnThis paper deals with demographic risk analysis in Enhanced Pensions, i.e. Long Term Care (LTC) insurance covers for retired. Both disability and longevity risk affect such a cover. Specifically, we concentrate on the risk of systematic deviations between projected and realised Specifically, we concentrate on the risk of systematic deviations between projected and realised mortality and disability, adopting a multiple scenarios approach. To this purpose we study the behaviour of the random risk reserve. Moreover, we analyse the effect of demographic risk on Risk-Based Capital requirements considering different time horizons and confidence levels and explaining how they can be reduced through either safety loading and reinsurance strategy. A profit analysis is also considered

Maximum Market Price of Longevity Risk Under Solvency Regimes: The Case Of Solvency II

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

Biometric risk analysis and solvency requirements in LTC insurance

Università degli studi di Roma “La Sapienza