Experience shows that static life tables overestimate death probabilities. As a consequence of this overestimation the premiums for annuities, pensions and life insurance are not what they actually should be, with negative effects for insurance companies or policy-holders. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality. Recent papers on the topic look for the development of new methods to deal with this dynamism.Most methods used in dynamic tables are parametric, apply traditional mortality laws and then analyze the evolution of estimated parameters with time series techniques. Our contribution consists in extending and applying Lee-Carter methods to Spanish mortality data, exploring residuals and future trends.

Dynamic life tables arise as an alternative to the standard (static) life table with the aim of incorporating the evolution of mortality over time. The parametric model introduced by Lee and Carter in 1992 for projected mortality rates in the US is one of the most outstanding and has been largely used since then. Different versions of the model have been developed but all of them, together with other parametric models, consider the observed mortality rates as independent observations. This is a difficult hypothesis to hold when looking at the graph of the residuals obtained with any of these methods.Methods of adjustment and prediction based on geostatistical techniques which exploit the dependence structure existing among the residuals are an alternative approach to classical methods. Dynamic life tables can be considered as a two-way table on a grid equally spaced in either the vertical (age) or horizontal (year) direction, and the data can be decomposed into a deterministic large-scale variation (trend) plus a stochastic small-scale variation (residuals). Preprint submitted to Insurance: Mathematics and EconomicsFebruary 8, 2010Our contribution consists of applying geostatistical techniques for estimating the dependence structure of the mortality data and for prediction purposes, also including the influence of the year of birth (cohort). We compare the performance of this new approach with different versions of the Lee-Carter model. Additionally, we obtain bootstrap confidence intervals for predicted q xt resulting from applying both methodologies, and we study their influence on the predictions of e 65t and a 65t .

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The nonparametric graduation of mortality data aims to estimate death rates by carrying out a smoothing of the crude rates obtained directly from original data. The main difference with regard to parametric models is that the assumption of an age-dependent function is unnecessary, which is advantageous when the information behind the model is unknown, as one cause of error is often the choice of an inappropriate model. This paper reviews the various alternatives and presents their application to mortality data from the Valencia Region, Spain. The comparison leads us to the conclusion that the best model is a smoothing by means of Generalised Additive Models (GAM) with splines. The most interesting part of this paper is the development of a plan that can be applied to mortality data for a wide range of age groups in any geographical area, allowing the most appropriate table to be chosen for the data in hand.