Surplus analysis for variable annuities with a GMDB option

In this paper, we analyze the insurance surplus for a Variable Annuity contract with a Guaranteed Minimum Death Benefit (GMDB) option. Initially, we derive the first two moments of the distribution of the surplus; and subsequently, we develop the whole distribution using a stochastic model which involves an integrated analysis of financial and mortality risk for a portfolio of annuities with GMDB embedded options. We offer a model according which the premium can be modified as per the forecasts of mortality probabilities, interest rate and fund evolution. Moreover, the study enables us to determine the premium that leads to a required probability of insolvency, and so it can be used for an evaluation of the adequacy of solvency. Numerical examples illustrate the results

Lee Carter mortality forecasting: application to the Italian population

In this paper we investigate the feasibility of using the Lee-Carter methodology to construct mortality forecasts for the Italian population. We fit the model to the matrix of Italian death rates for each gender from 1950 to 2000. A time-varying index of mortality is forecasted in an ARIMA framework and is used to generate projected life tables. In particular we focus on life expectancies at birth and, for the purpose of comparison, we introduce an alternative approach for forecasting life expectancies on a period basis. The resulting forecasts generated by the two methods are then compared

Mortality risk and the valuation of annuities with guaranteed minimum death benefit options: application to the Italian population

In this note, we describe the payoff of Guaranteed Minimum Death Benefit options (GMDB) embedded in annuity contracts and discuss their valuation using data for the Italian male population as a case study. These put options have stochastic maturity dates due to the involuntary exercise at the moment of death. We value the GMDB as a weighted average price of a set of deterministic put options with different maturity dates, where the weights are the probability of death at every date. We take into account the mortality risk and investigate the sensitivity of the price of the option to changes in mortality probability using both deterministic and stochastic approaches

Forecasting multiple functional time series in a group structure: an application to mortality’

When modeling sub-national mortality rates, we should consider three features: (1) how to incorporate any possible correlation among sub-populations to potentially improve forecast accuracy through multi-population joint modeling; (2) how to reconcile sub-national mortality forecasts so that they aggregate adequately across various levels of a group structure; (3) among the forecast reconciliation methods, how to combine their forecasts to achieve improved forecast accuracy. To address these issues, we introduce an extension of grouped univariate functional time series method. We first consider a multivariate functional time series method to jointly forecast multiple related series. We then evaluate the impact and benefit of using forecast combinations among the forecast reconciliation methods. Using the Japanese regional age-specific mortality rates, we investigate one-step-ahead to 15-step-ahead point and interval forecast accuracies of our proposed extension and make recommendations

A comparative study of parametric mortality projection models

The relative merits of different parametric models for making life expectancy and annuity value predictions at both pensioner and adult ages are investigated. This study builds on current published research and considers recent model enhancements and the extent to which these enhancements address the deficiencies that have been identified of some of the models. The England & Wales male mortality experience is used to conduct detailed comparisons at pensioner ages, having first established a common basis for comparison across all models. The model comparison is then extended to include the England & Wales female experience and both the male and female USA mortality experiences over a wider age range, encompassing also the working ages

llc: a collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms

We implement a specialised iterative regression methodology in R for the analysis of age-period mortality data based on a class of generalised Lee-Carter (LC) type modelling structures. The LC-based modelling frameworks is viewed in the current literature as among the most efficient and transparent methods of modelling and projecting mortality improvements. Thus, we make use of the modelling approach discussed in Renshaw and Haberman (2006), which extends the basic LC model and proposes to make use of a tailored iterative process to generate parameter estimates based on Poisson likelihood. Furthermore, building on this methodology we develop and implement a stratified LC model for the measurement of the additive effect on the log scale of an explanatory factor (other than age and time). This modelling methodology is implemented in a publically available collection of programming functions that facilitate both the preparation of mortality data and the fitting and analysis of the given log-linear modelling structures. Also, the package incorporates methods to produce forecasts of future mortality rates and to compute the corresponding future life expectancy

The implication of the hyperbolic discount model for annuitisation decisions

The low demand for immediate annuities at retirement has been a long-standing puzzle. We show that a hyperbolic discount model can explain this behaviour and results in the attractiveness of long-term deferred annuities. With a set of benchmark assumptions, we find that retirees would be willing to pay a much higher price than the actuarial fair price for annuities with longer deferred periods. Moreover, if governments were to introduce a pre-commitment device which requires pensioners to make annuitisation decisions around ten years before retirement, the take up rate of annuities could become higher

On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling

This paper provides a comparative study of simulation strategies for assessing risk in mortality rate predictions and associated estimates of life expectancy and annuity values in both period and cohort frameworks

Coherent modeling of mortality patterns for age-specific subgroups

The recent actuarial literature has shown that mortality patterns and trajectories in closely related populations are similar in some respects and that small differences are unlikely to increase in the long run. The common feeling is that mortality forecasts for individual countries could be improved by taking into account the patterns from a larger group. Starting from this consideration, we apply the three-way Lee–Carter model to a group of countries, by extending the bilinear LC model to a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. From a methodological point of view, there are several issues to deal with when focusing on such kind of data. In the presence of a three-way data structure, several choices on the pretreatment of the data could affect the whole modeling process. This kind of analysis is useful to assess the source of variation in the raw mortality data, before the extraction of the rank-one components by the LC model. The proposed procedure is used to extract an ad hoc time mortality trend parameter for age-specific subgroups. The results show that the proposed strategy leads to a more coherent description of mortality for age-specific subgroups