There are two fundamentally different ways of thinking about how mortality evolves over time: (a) think of mortality as a time series (the approach of the Lee-Carter model and its generalizations in the Cairns-Blake-Dowd family); (b) think of mortality as a smooth surface (the approach of the 2D P-spline models of Currie, Durban and Eilers and the smooth versions of the Lee-Carter model).

In a time-series model the mortality rates of the population are presumed to follow an underlying process.  But how do we simulate observed rates in a smoothed model which has no such process?  In this post we describe how we can simulate future sample paths of mortality in this second family.  An illustration from a smoothed…

When investigating risk in an annuity portfolio, a key task is to simulate the future lifetime for each annuitant.  Survival models make this particularly easy, as covered in an earlier posting on simulating lifetimes.

One of the first things which strikes practitioners is that volatility in run-off valuations increases with the average age of a portfolio.  The reason for this is that the variation in future lifetime gets larger relative to the average future lifetime.  One way of looking at this is to use the coefficient of variation, which is simply the standard error of the future lifetime divided by the mean:

coefficient of variation = standard error / mean

The coefficient of variation is normalised in that…