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Analysis of VaR-iance

In recent years we have published a number of papers on stochastic mortality models. A particular focus has been on the application of such models to longevity trend risk in a one-year, value-at-risk (VaR) framework for Solvency II. However, while a small group of models has been common to each paper, there have been changes in the calculation basis, most obviously where updated data have been used.

Written by: Stephen Richards

Fathoming the changes to the Lee-Carter model

Ancient Greek philosophers had a paradox called "The Ship of Theseus"; if pieces of a ship are replaced over time as they wear out until every one of the original components is gone, is it still the same ship? At this point you could be forgiven for thinking (a) that this couldn't possibly be further removed from mortality modelling, and (b) that I had consumed something a lot more potent than tea at breakfast.

Written by: Stephen Richards

Signal or noise?

Each year since 2009 the CMI in the UK has released a spreadsheet tool for actuaries to use for mortality projections. I have written about this tool a number of times, including how one might go about setting the long-term rate. The CMI now wants to change how the spreadsheet is calibrated and has proposed the following model in CMI (2016a):

$\log m_{x,y} = \alpha_x + \beta_x(y-\bar y) + \kappa_y + \gamma_{y-x}\qquad (1)$

Written by: Stephen Richards

The CMI is the part of the UK actuarial profession which collates mortality data from UK life offices and pension consultants. Amongst its many outputs is an Excel spreadsheet used for setting deterministic mortality forecasts. This spreadsheet is in widespread use throughout the UK at the time of writing, not least for the published reserves for most insurers and pension schemes.

Written by: Stephen Richards

Working with constraints

Regular readers of this blog will be aware of the importance of stochastic mortality models in insurance work.
Written by: Stephen Richards

Excel's limits

We have written in the past about some of the reasons why we don't use Excel to fit our models.  However, we do use Excel for validation purposes — fitting models using two entirely separate tools is a good way of checking production code.  That said, there are some important limits to Excel, especially when it comes to fitting projection models.
Written by: Stephen Richards

(Un)Fit for purpose

Academics lay great store by anonymous peer review and in openly publishing their results.  There are good reasons for this — anonymous peer review allows expert third parties (usually two) to challenge assumptions without fear of retribution, while open publishing allows others to test things and find their limitations.
Written by: Stephen Richards

The perils of parameter interpretation

With some notable exceptions, such as the Kaplan-Meier estimator, most mortality models contain parameters. In a statistical model these parameters need to be estimated, and it is a natural thing for people to want to place interpretations on those parameter estimates. However, this can be tricky, as parameters in a multi-parameter model are dependent on each other.

Written by: Stephen Richards

Volatility v. Trend Risk

The year 1992 was important in the development of forecasting methods: Ronald Lee and Lawrence Carter published their highly influential paper on forecasting US mortality.
Written by: Iain Currie