### Parameterising the CMI projection spreadsheet

#### (May 18, 2016)

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.

Following Willets (1999), the basic unit of the CMI spreadsheet is the mortality-improvement rate:

$1 - \frac{q_{x,t}}{q_{x,t-1}}\qquad(1)$

where $$q_{x,t}$$ is the probability of death aged $$x$$ in year $$t$$, assuming a life is alive at the start of the year.