Analysis of VaR-iance

(Mar 13, 2018)

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.  Sometimes these changes stemmed from more data being available, but, as Richard Willets covered in his blog, the ONS also restated the population estimates following the 2011 census.  This makes it tricky to compare results between papers. We therefore thought it would be instructive to do a step-by-step analysis…

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Tags: Lee-Carter, value-at-risk, longevity trend risk, Solvency II

VaR for longevity trend risk

(Dec 5, 2012)

Last month Stephen, Iain and Gavin presented their paper on putting longevity trend risk into a one-year, value-at-risk (VaR) framework.  The presentations were made to audiences of actuaries in Edinburgh and London, and the video of the London debate is now available online.  Copies of the opening speech and slides are available for download on the right.

On a related note, InsuranceERM has also published an article on the VaR framework, which is summarised in an earlier posting.

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Tags: longevity trend risk, VaR, value-at-risk

Discounting longevity trend risk

(Nov 12, 2012)

Establishing the capital requirement for longevity trend risk is a thorny problem for insurers with substantial pension or annuity payments.  In a previous posting I looked at the link between capital requirement and age, as well as the importance of model risk.  However, another important factor is the discounting function used for future cashflows.  This is illustrated in Figure 1, which shows the capital requirements implied by stressing the longevity trend over the lifetime of the annuitant.  This is done for the same projection model at various discount rates.  Besides the pattern with age, the most obvious feature is the strong dependence of the capital requirement on the discount rate used.

Figure…

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Tags: Solvency II, ICA, longevity trend risk, yield curve

Trend risk and age

(May 12, 2012)

There are several ways of looking at longevity trend risk, as covered in our recent seminar. However, regardless of how you choose to look at this risk, there are some pitfalls to watch out for. By way of illustration, we will consider here the capital requirements under the stressed-trend approach to longevity risk, although the basic points apply to most approaches.

Figure 1 shows the capital requirements implied by stressing the longevity trend over the lifetime of the annuitant. This is the so-called run-off approach, as opposed to the one-year, value-at-risk approach required by Solvency II (or ICA in the United Kingdom). The first aspect of Figure 1 is how different the various capital requirements are…

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Tags: Solvency II, ICA, longevity trend risk, model risk

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