# Report On Impact Of Mortality On Annuity: 736575

Report On Impact Of Mortality On Annuity

## 1.0.            Introduction

Annuity is a product offered by financial institutions that pays subscribers predetermined fixed amounts of money over a predetermined regular period of time. It is a popular product for retirees and pensioners. Rates of annuity products are determined by a number of factors such as age and income. Identifying such factors is a cog in setting appropriate rates for the annuity product. This report will look at whether mortality rates can affect annuity rates and if so, how mortality should be handle. Mortality rate is a demographic measure that indicates the percentage of death in a population. The association of old age and death thus brings mortality rate and annuity together. If mortality varies over time, then it can be an indicator of annuity rates.

## 2.0.            Methods And Results

This report considered two models of analysis:

### 2.1.            Lee Carter Model

A stochastic model developed in 1992, Lee Carter model is used to predict future mortality rates of a given population.

Time series models are used in the model to make future predictions.

Figure i

The output from the Lee-Carter Modeling in R is represented by the plot in figure i above. The Kappa plot indicates a decrease in the rate of mortality over the years while the Alpha plot indicates that the mortality curve has a universal shape.  Improvements in mortality decrease with increase in age of an individual in the given population as shown by the Beta plot. Thus, from the Kappa plot we can conclude that mortality changes with time and a stochastic modeling approach would be sufficient for better setting of annuity rates.

Using and ARMA model with p = 1 and q = 1, generated plot took the form of a Beta plot as shown in the figure below:

Figure ii

The plot shows a decrease in mortality improvements with increase in age.

### 2.2.            Generalized Linear Model

A Poisson based Generalized Linear Model is used to model mortality rate. The model took the form:

Dx;t = Poisson (Ex;tMx;t)

The Poisson model has deviance of 1362873 compared to the models null deviance that is equal to 230294974.This indicates the model’s ability to efficiently predict values of future mortality rates as it points to high accuracy.

For the prediction of the mortality for the year 2016 from the data provided (1933-2015), the plot below is obtained. This is the plot for the universal mortality curve.

Figure iii

## 3.0.            Discussion

From the deviance values of the models above it is clear that the Poisson Generalized Linear Model has a higher level of accuracy as compared to the Lee-Carter Model. Cohort effect explains the variations in the characteristics of individuals connected to each other by a shared experience.

The analysis of male and female datasets was done together as the “Total” variable. This helps in obtaining the complete view of the population as opposed to segmented data analysis. analysis. The age was also considered for all ages to provide complete inference about the population.

## 4.0.             Conclusion

The mortality rate, from the analysis of the U.S.A mortality data, changes with time. This therefore implies that mortality rate should be factored in the computation of the annuity rates. We can thus conclude that the use of the Poisson Generalized Linear Model for the prediction of future mortality rates would produce accurate values which can be factored in the calculations of the annuity rates.