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This paper aims to measure the financial impact on social security system of a recently proposed indexation mechanism for retirement age by considering the Italian longevity experience. The analysis is motivated by the progressive increase in life expectancy at advanced age, which is rapidly bringing to the fore noticeable socio-economic consequences in most industrialized countries. Among those, the impact on National Social Security systems is particularly relevant if people live longer than expected; this will lead to greater financial exposure for pension providers.

Referring to the Italian population for illustrative purposes, the authors contemplate different scenarios for mortality projection methods and for the implementation of pension age shift while accounting for gender and cohort gaps and model risk. Synthetic indicators to measure the impact of the indexation mechanism on social security system are introduced on the basis of pension cash flows.

An indexation policy that manages gender gap while adjusting retirement age for varying life expectancy is proposed. As a result, sustainability of public retirement expenditure is improved.

The paper is a concise scenario analysis of the reduction of costs and risks that pension providers would have if the system resorted to link retirement age to life expectancy. The ideas fostered by the paper follow a recent proposal of the Authors on a flexible retirement scheme that deals with model risk for mortality projection and accounts for gender gap in mortality rates.

The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless, the difference between the reference population of the hedging instrument and the population of members of a pension plan, or the beneficiaries of an annuity portfolio, determines a significant heterogeneity causing the so-called basis risk. In particular, it is shown that if insurers use financial instruments based on national indices to hedge longevity risk, this hedge can become imperfect. For this reason, it is fundamental to arrange a model allowing to quantify the basis risk for minimising it through a correct calibration of the hedging instrument.

The paper provides a framework for measuring the basis risk impact on the. To this aim, we propose a model that measures the population basis risk involved in a longevity hedge, in the functional data model setting. hedging strategies.

The innovative contribution of the paper occurs in two key points: the modelling of mortality and the hedging strategy. Regarding the first point, the paper proposes a functional demographic model framework (FDMF) for capturing the basis risk. The FDMF model generally designed for single population combines functional data analysis, nonparametric smoothing and robust statistics. It allows to capture the variability of the mortality trend, by separating out the effects of several orthogonal components. The novelty is to set the FDMF for modelling the mortality of the two populations, the hedging and the exposed one. Regarding the second point, the basic idea is to calibrate the hedging strategy determining a suitable mixture of q-forwards linked to mortality rates to maximise the degree of longevity risk reduction. This calibration is based on the key q-duration intended as a measure allowing to estimate the price sensitivity of the annuity portfolio to the changes in the underlying mortality curve.

The novelty lies in linking the shift in the mortality curve to the standard deviation of the historical mortality rates of the exposed population. This choice has been determined by the observation that the shock in a mortality rate is age dependent. The main advantage of the presented framework is its strong versatility, being the functional demographic setting a generalisation of the Lee-Carter model commonly used in mortality forecasting, it allows to adapt to different demographic scenarios. In the next developments, we set out to compare other common factor models to assess the most effective longevity hedge. Moreover, the parsimony for considering together two trajectories of the populations under consideration and the convergence of long-term forecast are important aspects of our approach.

The demographic risk is the risk due to the uncertainty in the demographic scenario assumptions by which life insurance products are designed and valued. The uncertainty lies both in the accidental (insurance risk) and systematic (longevity risk) deviations of the number of deaths from the value anticipated for it. This last component gives rise to the risk due to the randomness in the choice of the survival model for valuations (model risk or projection risk). If the insurance risk component can be assumed negligible for well‐diversified portfolios, as in the case of pension annuities, longevity risk is crucial in the actuarial valuations. The question is particularly decisive in contexts in which the longevity phenomenon of the population is strong and pension annuity portfolios constitute a meaningful slice of the financial market – both typical elements of Western economies. The paper aims to focus on the solvency appraisal for a portfolio of life annuities, deepening the impact of the demographic risk according to suitable risk indexes apt to describe its evolution in time.

The financial quantity proposed for representing the economic wealth of the life insurance company is the stochastic surplus, and the paper analyses the impact on it of different demographic assumptions by means of risk indicators as the projection risk index, the quantile surplus valuation and the ruin probability. By means of the proposed models, the longevity risk is mainly taken into account in a stochastic scenario for the financial risk component, in order to consider their interactions, too. In order to furnish practical details significant in the portfolio risk management, several numerical applications clarify the practical meaning of the models in the solvency context.

This paper studies the impact on the portfolio surplus of the systematic demographic risk, taking into account their interaction with the financial risk sources. In this order of ideas, the internal risk profile of a life annuity portfolio is deeply investigated by means of suitable risk indexes: in a solvency analysis perspective, some possible scenarios for the evolution of death rates (generated by different survival models) are considered and this paper evaluates the impact on the portfolio surplus caused by different choices of the demographic model. The first index is deduced by a variance decomposition formula, the other ones involve the conditional quantile calculus and the ruin probability. Such indexes constitute benchmarks, whose conjoined use provides useful information to the meeting of the solvency requirements.

With respect to the recent actuarial literature, in which the most important contribution on the surplus analysis has been given by Lisenko et al. – where the analysis focuses on the financial aspect applied to portfolios of temporary and endowment contracts – the paper considers life annuity portfolios, taking into account the effect of the systematic demographic risk and its interactions with the financial risk components.

The determination of the capital requirements represents the first Pillar of Solvency II. The main purpose of the new solvency regulation is to obtain more realistic modelling and assessment of the different risks insurance companies are exposed to in a balance‐sheet perspective. In this context, the Solvency Capital Requirement (SCR) standard calculation is based on a modular approach, where the overall risk is split into several modules and submodules. In Solvency II, standard formula longevity risk is explicitly considered. The purpose of this paper is to look at the backtesting approach for measuring the consistency of SCR calculations for life insurance policies.

A multiperiod approach is suggested for correctly calculating the SCR in a risk management perspective, in the sense that the amount of capital necessary to meet company future obligations year by year until the contract will be in force has to be assessed. The backtesting approach for measuring the consistency of SCR calculations for life insurance policies represents the main contribution of the research. In fact this kind of model performance is generally specified in the VaR validation analysis. In this paper, this approach is considered for testing the ex post performance of SCR calculation methodology.

The backtesting framework is able to measure, from time to time, if the insurer has allocated more or less capital to support his in‐force business, with adverse effects on free reserves and profitability or solvency.

The paper shows that the forecasting performance is an important aspect to assess the effectiveness of the model, a poor performance corresponding to a biased allocation of capital.

The backtesting approach for measuring the consistency of SCR calculations for life insurance policies represents the main contribution of the research. In fact this kind of model performance is generally specified in the VaR validation analysis. Recently, Dowd et al. have proposed it for verifying the goodness of mortality models and now, in this paper, this approach is considered for testing the ex post performance of SCR calculation methodology.