Category: longevity

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The Hedging Fallacy

In our discussions with equity release actuaries, Dean and I have often come across some recurring arguments.

An example is what we might call the ‘hedging fallacy’ – the argument that we can’t apply B76 (or BS) to value equity release NNEGs because these option price formulas are derived under the assumption that the underlying variable, in this case, forward contracts on residential property, can be hedged. This assumption is obviously empirically invalid, so the argument goes, therefore we shouldn’t use B76/BS. And the argument (often) continues, we should then throw away B76/BS and use the discounted projection approach instead. And thankfully, the discounted projection approach delivers much lower NNEG values. So there is nothing to worry about – all that undervalued NNEG stuff is overhyped.

This argument is false, but it is false in a number of interesting ways.

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Diamond Princess update

Data so far suggests that of the 3,711 people on the Diamond Princess cruise ship, 705 contracted the virus, i.e. 19%. Much higher than in any place in China, as we have stated passim, but then a cruise ship is a confined space with a lot of people in it. So far, 6 people appear to have died, which is 0.85% of those diagnosed. The mortality relative to the whole population is therefore 6 divided by 3,711, i.e. 0.16%.

These figures conflict somewhat with the crude distribution we published here, but we did say to treat all figures with caution. There is a conflict because, as is well known, mostly old people like us go on cruises, but we are seeing nothing like an 18% case fatality rate.

[EDIT] A useful paper on the Diamond Princess age distribution is here. Table copied below.

Age group Symptomatic cases Asymptomatic cases 1 Total Crude asymptomatic ratio 2 Persons aboard3
0-9 0 1 1 100% (95%CI: 2.5%, 100%) 16
10- 1 1 2 50.0% (95%CI: 1.3%, 98.7%) 23
20- 18 2 20 10.0% (95%CI: 1.2, 31.7%) 347
30- 18 5 23 21.7% (95%CI: 7.5%, 43.7%) 429
40- 18 7 25 28.0% (95%CI: 12%, 49.4%) 333
50- 27 22 49 44.9% (95%CI: 30.1%, 59.8%) 398
60- 73 56 129 43.4% (95%CI: 2.5, 100%) 924
70- 92 136 228 59.6% (95%CI: 53.0%, 66.1%) 1015
80- 27 25 52 48.1% (95%CI: 34.0%, 62.3%) 215
90- 2 0 2 0% (95%CI: 2.5%, 84.2%) 11
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CBDX – A Workhorse Mortality Model

(Mortality geeks only)

David Blake, Andrew Cairns and yours truly have just finished an article outlining a new(ish) mortality, model, CBDX. The purpose of the model is to offer a workhorse model that spans middle age as well as old age.

To recap: our original Cairns-Blake-Dowd (CBD) mortality model was specifically designed to capture the mortality behaviour of older people, e.g., people over 50. We were thinking of annuitants but equally it could apply to equity release borrowers, who must be at least 55.

Our original model had only two period (or passage of time) effects, the second of which enters the model through a coefficient that is a linear function of age. We then generalised then it to a CBD family consisting of 3 related models: M5, which is equivalent to a reconfigured CBD; M6, which is M5 plus a cohort (year of birth) effect; and M7, which is M6 plus a further period effect, which enters the model through a coefficient that is a quadratic function of age. More details on these models can be found here.

In subsequent work we discovered (to our surprise) that M7 performed robustly well across a number of different data sets. We had not expected a model with a quadratic function to perform as well as it did.

However, these models do not tend to perform well over age ranges that include younger ages. So one would not use the CBD family for, say, a model of a DC pension started at a youngish age. Andrew, David and I have long felt the need to remedy that limitation.

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