Albina Orlando

Solvency analysis and demographic risk measures

Purpose - 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. Design/methodology/approach - 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. Findings - 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. Originality/value - With respect to the recent actuarial literature, in which the most important contribution on the surplus analysis has been given by Lisenko

Measuring demographic uncertainty via actuarial indexes

Aim of the paper is the analysis of the behaviour of risk filters connected to the demographic risk drivers for a portfolio of life annuities. The model, easily suitable to the rase of pension annuities, involves the evolution in time of the mortality rates, taking into account the randomness of the financial scenario. Within this context, the uncertainty in the choice of the deiriograpllic scenario is measured and the analysis is also supported by the VaR sensitivity to this risk source.

A financial analysis of surplus dynamics for deferred life schemes

The paper investigates the financial dynamics of the surplus evolution in the case of deferred life schemes, in order to evaluate both the distributable earnings and the expected worst occurence for the portfolio surplus. The evaluation is based on a compact formulation of the insurance surplus defined as the difference between accrued assets and present value of relevant liabilities. The dynamic analysis is performed by means of Monte Carlo simulations in order to provide a year-by-year valuation. The analysis is applied to a deferred life scheme exemplar, considering that the selected contract constitutes the basis for many life insurance policies and pension plans. The evaluation is put into an asset and liability management decision-making context, where the relationships between profits and risks are compared in order to evaluate the main features of the whole portfolio.

Life Annuity Portfolios: Risk-Adjusted Valuations and Suggestions on the Product Attractiveness

Solvency assessing is a compelling issue for the insurance industry, also in light of the current international risk-based regulations. Internal models have to take into account risk/profit indicators, in order to provide flexible tools aimed at valuing solvency. We focus on a variable annuity with an embedded option involving a participation level which depends on the period financial result. We realize a performance evaluation by means of a suitable indicator, which properly captures both financial and demographic risk drivers. In fact, in the case of life annuity business, assessing solvency has to be framed within a wide time horizon, where specific financial and demographic risks are realized. In this order of ideas, solvency indicators have to capture the amount of capital to cope with the impact of those risk sources over the considered period. The analysis is carried out in accordance with a management perspective, apt to measure the business performance, which requires a correct risk control; in particular we present a study of the dynamics of the profit realized per unit of the total financial value of the contract. On the other hand, the consumer profitability is also measured by means of an utility-equivalent fixed life annuity. Ac-cording to the insureds point of view, we measure their perception of the contract profitability within the expected utility approach.

Profitability vs. Attractiveness Within a Performance Analysis of a Life Annuity Business

Combining insurer’s profitability with products’ attractiveness in terms of marketing competitiveness is a critical issue within the risk/profit management of an insurance business. In particular life insurance products are characterized by the presence of financial and demographic risk sources, whose combined effect requires suitable management strategies. This paper deals with the impact of the load factor on life annuity portfolio performance from the insurers point of view. The aim is to build a performance indicator that clearly points out the role of the load factor in the performance making, giving to it a central role in the company management strategy. Such index is characterized by a simple mathematical structure and fits to the purpose: in fact it provides clear indications to the manager about the influence of the load factor on the performance of the life annuity business line.

Measuring and Managing the Longevity Risk: An Empirical Evidence From the Italian Pension Market

This paper deals with the problem of quantifying the longevity impact for defined contribution pension funds in a stochastic environment. In the accumulation phase it is well known that, in presence of a benefit guarantee, the investment risk dominates the demographic one. However, if the generic subscriber life expectancy increases, it is very likely that, in the decumulation phase, the wealth accrued will not be able to cover the liabilities of the fund. For this reason, the fund will be forced to set aside more resources in order to front its liabilities exposing itself to greater financial risk. In this paper we study the interaction between financial risk and longevity: based on the Italian experience for both financial and demographic factors, this work aims to measure the impact of longevity on the financial factor.

Empirical Evidences on Predictive Accuracy of Survival Models

The paper focuses on a stochastic proportional hazard model depicting the evolution of the force of mortality; in particular the real data are plotted against a specific survival model by means of the stochastic process that describes their ratio. The predictive accuracy of the survival model is investigated, since, by means of the calibrated “ratio process”, its forecasting skills are assessed. A statistical analysis is developed in order to test the capacity the assumed survival model has to follow the real behavior of the observed data.

Stochastic Actuarial Valuations in Double-Indexed Pension Annuity Assessment

The paper deals with the performance analysis of a portfolio of participating survival-indexed annuities within a riskiness context, set out by the adverse deviations of the demographic and financial bases. The Authors deepen the interactions between the risk due the random fluctuations of the dynamic of the capital returns and the risk due to the systematic random fluctuations of the lifetime evolutionary trend.

Capital requirements for aggregate risks in long term living products: A stochastic approach

Referring to the Solvency II regulation, aim of the paper is to obtain an estimate for the Solvency Capital Requirement of a life annuity portfolio when stochastic interest and mortality rates are considered. We propose a computationally tractable approach that yields an estimate for the required solvency capital when mortality and interest rates are forecasted by means of diffusion processes. To this aim we determine the capital requirements for each considered risk factor and then we compute the Global Solvency Capital Requirement. Numerical applications analyzing the effect of the choice of different scenarios on the Global SCR quantification are proposed.

Further Remarks on Risk Profiles for Life Insurance Participating Policies

This paper deals with the calculation of suitable risk indicators for Life Insurance policies in a Fair Value context. In particular, after determining the quantile reserve for Life Insurance Participating Policies, the role of the term structure of mortality rates is analyzed in risk determinations. Numerical results are investigated in order to determine not only suitable risk indicators, but also the mortality risk impact in this context.