Hedging or betting?

(Sep 27, 2018)

Last week I presented at Longevity 14 in Amsterdam.  A recurring topic at this conference series is index-based approaches to managing longevity risk.  Indeed, this topic crops up so reliably, one could call it a hardy perennial.

For a long time insurers and pension schemes were sceptical of derivatives-based solutions to managing longevity risk.  Part of this scepticism was due to basis risk - why enter into a contract based on population mortality when a portfolio has very specific mortality characteristics?  In particular, most portfolios tend to have a concentration of risk in a relatively small subset of lives.  Another reason for scepticism was price - it was often cheaper to reinsure the entire risk…

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Tags: basis risk, concentration risk, model risk

Socio-economic differentials: convergence and divergence

(Jun 18, 2018)

Many western countries, including the UK, have recently experienced a slowdown in mortality improvements.  This might lead to the conclusion that the age of increasing life expectancies is over.  But is that the case for everyone?  Or are there some groups in the UK who are still experiencing mortality improvements?  The short answer is that mortality rates are still falling for the least deprived half of the population in England, while mortality improvements since 2011 have been virtually zero for the most deprived third.  This has important consequences for reserving for pensions and annuities, so let us explore in a bit more detail.  The findings in this blog are based on some early results of research…

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Tags: mortality convergence, mortality improvements, concentration risk, basis risk

How much data do you need?

(Aug 30, 2017)

There are two common scenarios when an actuary has to come up with a mortality basis for pensioners or annuitants:

  1. For a portfolio of liabilities already owned, e.g. an insurer's existing annuities in payment or a pension scheme's pensions in payment.
  2. For a portfolio of liabilities where the risk is to be transferred, e.g. an insurer or reinsurer looking to price a buy-out or longevity swap.

Leaving aside questions of data quality, in each case the actuary is faced with the same question: is the portfolio's experience data large enough to rely on? And if there isn't enough experience data, what does the actuary do instead?

At one extreme consider a pension scheme with a hundred pensioners. With an average of around…

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Tags: credibility, basis risk, concentration risk

Reverse Gear

(Dec 8, 2015)

Against a background of long-term mortality improvements it is understandable to expect that societal change and developments in health care will be agents of progress. Recent research from Princeton Professor of Economics Anne Case and Nobel prize-winning economist Angus Deaton jolts such complacency in the starkest way. It reveals that since the late nineties, the all-cause mortality improvements experienced by white non-Hispanic Americans in midlife (ages 45 to 54) have not simply slowed, but slammed into reverse.

It quickly becomes clear that this research contains a telling illustration of basis risk. The researchers note that the scale of the effect had been missed since it played out so strongly…

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Tags: longevity, mortality improvements, mortality plasticity, basis risk

Haircut or hedge-trim?

(Jul 4, 2013)

Richard Willet's observation last year on the restatement of population estimates was picked up again recently by the BBC.  Amongst the implications of the missing nonagenarians are some potentially interesting consequences for index-based longevity hedges. These are derivative contracts based on population mortality data. The idea is that an organisation holding longevity risk, such as an insurer or pension fund, would buy or sell an appropriate instrument to transfer risk to an investor willing to take it. The portfolio being hedged will not have the same mortality dynamics as the population - so-called basis risk - but the idea is that the hedge will provide at least partial protection.


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Tags: ONS, longevity hedge, basis risk, S-forward

Risk and models under Solvency II

(Aug 21, 2011)

Insurers need to have internal models for their major risks. Indeed, both the Individual Capital Assessment (ICA) regime in the UK and the pending Solvency II rules in the EU demand that insurers have good models for their risks.

However, when building a model for mortality or any other kind of risk, you have a number of known issues in the modelling process:

  1. Model risk. You do not actually know what model structure is most appropriate for your portfolio or risk.  This is particularly keenly felt for mortality projections.
  2. Basis risk. Even if you have the correct model, you should be calibrating it using the same population you want to model. However, if you fit a model to the experience from one portfolio, yet use…

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Tags: ICA, Solvency II, model risk, basis risk, concentration risk, model points

Everything counts in large amounts

(Aug 8, 2011)

Models for projecting mortality are typically built using information on lives with deaths by age and gender.  However, this ignores an important risk factor for longevity, namely socio-economic group.  For annuity and pension reserving, therefore, it would be helpful to use such information when building stochastic projection models.  Actuaries have two routes whereby they can get proxy information for socio-economic group: pension size and geodemographics.

Typically such data is not available at the population level, but the CMI Pensioner dataset is one of the few with mortality data on both lives and amounts; we use these data for ages 60 to 90 and for years 1983 to 2006. Figure 1 shows observed log(mortality)…

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Tags: basis risk, piggyback model, amounts-weighted mortality

A basis point

(Jun 7, 2011)

In an earlier post I mentioned the advent of survivor forwards, or S-forwards, a derivative contract which could be used for hedging pension liabilities.  Survivor forwards appeared again in another post illustrating the financial impact of model risk.

A survivor forward defined on an index of, say, population mortality will give a large data set with considerable history on which to base a projection model.  However, a natural question is to ask how suitable such a contract would be for hedging pension or annuitant liabilities?  Figure 1 shows the Kaplan-Meier survival curve from age 70 for male annuitants born in 1928, together with the corresponding survival curve for males in England & Wales.


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Tags: survivor forward, S-forward, hedging, basis risk

Forecasting with limited portfolio data

(Sep 7, 2009)

In a recent post on basis risk in mortality projections, I floated the idea of forecasting with limited data and even suggested that it would be possible to use the method to produce a family of consistent forecasts for different classes of business.  The present post describes an example of how this idea works in practice.

Forecasting with limited data depends on the simple idea of using actual portfolio data to adjust a separate forecast made with some very much larger reference data set.  We use the following example:

  1. Reference data: CMI assured lives data between years 1950-2005, covering ages 40-89.  We assume the data have been graduated and a forecast has been made to 2048, say.  The output from this process…

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Tags: basis risk, mortality projections


(Jul 3, 2009)

Actuaries valuing pension liabilities need to make projections of future mortality rates.  The future is inherently uncertain, so it is best to use stochastic models of mortality.  Unfortunately, such models require a long enough time series, but few (if any) portfolios have such data.  In the UK actuaries typically rely on one of two alternative data sets: the England & Wales data from the ONS, which goes back to 1961, or the "assured lives" data from the CMI, which goes back to 1947.  An earlier post contains an animation showing how the CMI data has changed dramatically over this period.

However, a model for the mortality of one group may not be directly suitable for projecting the mortality…

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Tags: basis risk, CMI

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