### Signal or noise?

#### (Nov 25, 2016)

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):

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

which the CMI calls the APCI model.  $$m_x$$ is the central rate of mortality at age $$x$$ in year $$y$$ and $$\alpha_x$$, $$\beta_x$$, $$\kappa_y$$ and $$\gamma_{y-x}$$ are vectors of parameters to be estimated.  $$\bar y$$ is the average year, which is used to centre the time index around…

Tags: CMI, APCI, APC, Lee-Carter, Age-Period, smoothing

### 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.

### S2 mortality tables

#### (Feb 9, 2014)

The CMI has released the long-awaited S2 series of mortality tables based on pension-scheme data.  These are the first new tables since the CMI changed its status (the S2 series is only available to paying subscribers, unlike prior CMI tables).  A comparison of the main S2 mortality rates with the preceding S1 rates is given in Figure 1.

Figure 1. Ratio of S2 mortality rates to S1 rates. Source: Own calculations using S1PA and S2PA tables from the CMI.

As expected, there have been large reductions in mortality, especially for males - at ages 60-80 there has been a fall of at least 15%.  This age range is key for pension-scheme reserves and annuity profitability.  The S1 series has an effective date of 1st September…

### Benchmarking VaR for longevity trend risk

#### (Mar 1, 2013)

I recently wrote about an objective approach to setting the value-at-risk capital for longevity trend risk.  This approach is documented in Richards, Currie & Ritchie (2012), which was recently presented to a meeting of actuaries in Edinburgh.  One of the topics which came up during the discussion was how the answers from the value-at-risk (VaR) method squared with how life offices actually change their projection bases in practice.  In particular, commentators were interested in what might be regarded as a "real world" example of a sudden change in projection basis, and how this might compare with the results from the VaR framework.

As it happens, we do have an historical example to call upon, and furthermore…

### 2D or not 2D?

#### (Apr 24, 2012)

The Society of Actuaries (SOA) in North America recently published an exposure draft of a proposed interim mortality-improvement basis for pension-scheme work. The new basis will be called "Scale BB" and is intended as an interim replacement for "Scale AA".   Like Scale AA, the interim Scale BB is one-dimensional in age, i.e. mortality improvements vary by age and gender only. However, the SOA is putting North American actuaries on notice that a move to a two-dimensional projection is on the cards:

"the recommended replacement for Scale AA will likely be two-dimensional tables of gender/age/calendar year mortality improvement rates. RPEC encourages the developers of actuarial…

### All bases covered

#### (Apr 10, 2012)

It is fairly obvious by now that we are strong advocates for stochastic projection models. Such models crucially provide a basis with two components - a best-estimate force of mortality by age and year, and matching standard error values for the same 2D range. Not all bases derive from stochastic methods of course, and so called deterministic bases will produce a single estimate without uncertainty measures. A popular example of a deterministic basis in use is that from the CMI, which is updated each year in response to revised data from the ONS and is driven by a user-input expectation of the long-term mortality improvement rate.

Both types of basis are in common usage and are often applied in concert. One example…

Tags: mortality projections, CMI

### Survival models for actuarial work

#### (Dec 19, 2011)

The CMI recently asked for an overview note on survival models.  Since this subject is of wider actuarial interest, we wanted to make this publically available. An electronic copy can be downloaded from the link on the right.

Tags: CMI, survival models, mortality

### Currency devaluation

#### (Mar 17, 2011)

I have written before on aspects of the CMI's new deterministic projection model (some comments I made at a public meeting in January 2011 are available on the right).  One hoped-for goal was that the CMI 2010 model would become a "common currency" for communicating mortality-improvement bases ( Working Paper 41, sections 2.1-2.4).

The CMI 2010 model is now being used in company financial statements. A recent example is Prudential's statement about its allowance for future mortality improvements for annuities in the UK:

"The Continuous Mortality Investigation (CMI) model and Core Projection parameters have been reviewed and a custom parameterisation of the CMI model has been made where…

### Applying the brakes

#### (Jan 24, 2011)

The CMI has released a second version of its deterministic targeting model for mortality improvements.  This type of model is called an expectation, as the user must enter their belief for the long-term rate of mortality improvement to use the tool.  Expectations have their own unique features, as discussed in an earlier blog.  The CMI's tool has some unusual features, which I highlighted at the recent public meeting in Edinburgh.  A copy of these comments can be downloaded on the right.

However, there is one particular feature of the core model which must be emphasised, namely that it automatically projects decelerating rates of improvement.  By way of illustration, consider people born in 1946 who will attain…

### Laying down the law

#### (Dec 14, 2010)

In actuarial terminology, a mortality "law" is simply a parametric formula used to describe the risk.  A major benefit of this is automatic smoothing and in-filling for areas where data is sparse.  A common example in modern annuity portfolios is that there is often plenty of data up to age 75 (say), but relatively little data above age 90.

For example, if we use a parametric formula like the Gompertz law:

log μx = α + βx

then we can use a procedure like the method of maximum likelihood to estimate α and β.  Once we have these values, we can generate mortality rates at any age we require, not just the ages at which we have data.

But which mortality law should one use?  In a recent paper (Richards,…