Valeria D'Amato

Backtesting the solvency capital requirement for longevity risk

Purpose - 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. Design/methodology/approach - 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 Findings - 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. Practical implications - 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. Originality/value - 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

Adaptive Neuro-Fuzzy Inference Systems vs. Stochastic Models for Mortality Data

A comparative analysis is done between stochastic models and Adaptive Neuro–Fuzzy Inference System applied to the projection of the longevity trend. The stochastic models provides the heuristic rule for obtaining projections. In the context of ANFIS models, the fuzzy logic allows for determining the learning algorithm on the basis of the relationship between inputs and outputs. In other words the rule is here deducted by the actual mortality data, because this allows for fuzzy systems to learn from the data they are modelling. This is possible by computing the membership function parameters that best allow the associated fuzzy inference system to track the input/output data. The literature indicates that the self-predicting model of ANFIS is better than other models in a lot of fields. Shortcomings and advantages of both approaches are here highlighted.

The dependency premium based on a Multifactor Model for dependent mortality data

ABSTRACT As shown in the literature, the dependence structure in mortality data cannot be ignored in projecting future trends, in particular for a group of similar populations characterized by common long-run relationships. We propose a new multifactor model for capturing common and specific features of the trend over time. We implement the model and investigate its impact on actuarial valuations, through the introduction of the concept of the dependency premium.

Simulation Framework in Fertility Projections

By 1951, average fertility had fallen to just over two children per woman, and only five percent of children would die in their first ten years of life. A similar pattern of declining fertility and mortality rates, collectively known as the demographic transition, has been observed in every industrializing country. Financial projections for Social Security systems depend on many demographic, economic and social factors as well as the reduction of fertility rates and the ageing of a population. In order to address the need to develop reliable projections, it is unavoidable to detect appropriate measures to represent the future trends of the quantities of interest. The aim of the paper is apply to Italian data a mathematical scheme suitable for projecting the fertility rates and for measuring the uncertainty around these estimates. Finally a numerical application is provided.

Intensive Computational Forecasting Approach to the Functional Demographic Lee Carter Model

Several approaches have been developed for forecasting mortality using stochastic model. In particular, the Lee Carter model (1992) has become widely used and there have been various extensions and modifications proposed to attain a broader interpretation and to capture the main features of the dynamics of the mortality intensity. Hyndman and Ullah (2005). introduce a particular version of the Lee Carter methodology, the so-called Functional Demographic Model --FDM, the most accurate approach as regards some mortality data, particularly for longer forecast horizons where the benefit of a damped trend forecast is greater. The paper objective is properly to single out the most suitable model between the basic Lee Carter and the FDM to the Italian mortality data. A comparative assessment is made. Moreover, we provide information on the uncertainty affecting the forecasted quantities by using bootstrap technique. The empirical results are presented using a range of graphical analyses.