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Valuing liabilities with survival models

Regular readers of this blog will know that we are strong advocates of the benefits of modelling mortality in continuous time via survival models. What is less widely appreciated is that a great many financial liabilities can be valued with just two curves, each entirely determined by the force of mortality, \(\mu_{x+t}\), and a discount function, \(v^t\).

Written by: Stephen RichardsTags: survival curve, curve of deaths

Getting animated about longevity

We'll be the first to admit that what we have here doesn't exactly provide Pixar levels of entertainment. However, with the release of v2.7.9 users of the Projections Toolkit can now generate animations of fitted past mortality curves and their extrapolation into the future.
Written by: Stephen RichardsTags: survival curve, curve of deaths, mortality compression

Lost in translation

Actuaries have a long-standing habit of using different terminology to statisticians. This page lists some common terms used by actuaries in mortality work and their "translation" for a non-actuarial audience. The terms and notation are those used by actuaries in the UK, but in every country I have visited the local actuaries have used similar notation.

Table 1. Common actuarial terms and their definition for statisticians.

Written by: Stephen RichardsTags: central exposed-to-risk, curve of deaths, force of mortality, initial exposed-to-risk, mortality law, mortality rate, survival rates, waiting time, survival models

Run-off volatility

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.
Written by: Stephen RichardsTags: simulation, curve of deaths, coefficient of variation, ICA, Solvency II

Fifteen-year (h)itch

Effective risk modelling is about grouping people with shared characteristics which affect this risk.  In mortality analysis by far the most important risk factor is age, so it is not a good idea to mix the young and old if it can be avoided.  By way of illustration, Figure 1 shows that mortality rates increase exponentially over much of the post-retirement age range. 

Written by: Stephen RichardsTags: survival analysis, survival curve, curve of deaths

Mortality transformation

A tool often used by demographers is the distribution of age at death in a population.  This is known to actuaries as the curve of deaths, and the past 170 years have seen a rather remarkable transformation in this curve. 
Written by: Stephen RichardsTags: mortality transformation, curve of deaths, mortality compression