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

Twin Peaks

(Jun 15, 2017)

If you are over forty, the title of this blog will call to mind an iconic, sometimes disturbing, television series of the same name from 1990.  If you clicked on the link expecting murder, surreal horror and an undercurrent of sleaze, however, then this posting is as far away from all that as you are ever likely to get: setting capital requirements for life insurers.  Take a deep breath to recover from your crushing disappointment and let's get back to the day job…

Insurers in the EU operate under Solvency II, which is a one-year, value-at-risk regulatory regime.  The idea is that an insurer needs to hold reserves which will be sufficient to cover 99.5% of adverse scenarios over the coming year and still have enough…

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Tags: value-at-risk, bimodal distribution, Solvency II, model risk

Picking a Winner

(May 5, 2015)

So what will the winner of the battle of the UK General Election be able to tell us about projection modelling? I'm not talking about the parties who will gain a share of power after May 7th, but which of the polling organisations will most closely forecast the results.

The record of UK pollsters hit a memorable low in the 1992 General Election. In the week prior to the vote they were finding an average Labour lead of 2%, thus spectacularly failing to spot the actual outcome: a Tory win by almost 8%. With the benefit of hindsight, it is easy to see that their models were systematically wrong. The Market Research Society undertook a review of the debacle which identified both methodological and behavioural reasons. These…

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Tags: projections, model risk

(Un)Fit for purpose

(May 26, 2014)

Academics lay great store by anonymous peer review and in openly publishing their results.  There are good reasons for this - anonymous peer review allows expert third parties (usually two) to challenge assumptions without fear of retribution, while open publishing allows others to test things and find their limitations.  For example, the model from Lee & Carter (1992) has been thoroughly researched over the past two decades, and its limitations are well known.  However, the Lee-Carter model has stood the test of time in no small part because these limitations have been publicly documented by other researchers.

One advantage of all this open publication is that major problems can be spotted and brought…

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Tags: Lee-Carter, Renshaw-Haberman, model risk

VaR-iation by age

(Jan 12, 2013)

During the public discussions of our paper on value-at-risk for longevity trend risk, one commentator asked for a fuller presentation of VaR capital requirements by age. In the paper, as with our introductory overview, we used age 70 as a representative average age of an annuity portfolio.  However, annuity portfolios contain lives spanning a wide range of ages, so it is useful to examine how capital requirement might vary.  Figure 1 shows the VaR longevity-trend capital requirement by age for four different models.

Figure 1. 99.5% VaR capital requirement for longevity trend risk in a level pension paid to a single-life male annuitant. Temporary annuity to age 105, discounted at 3% per annum.  The capital…

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Tags: VaR, value-at-risk, model risk

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

Longevity trend risk under Solvency II

(Jan 18, 2012)

Longevity trend risk is different from most other risks an insurer faces because the risk lies in the long-term trajectory taken by mortality rates. This trend unfolds over many years as an accumulation of small changes, so a natural approach is to calculate reserves using a long-term stress projection from a stochastic model, as shown in Figure 1.

Figure 1. Central projection from a Lee-Carter model, together with the lower 99.5th confidence level derived from multiplying the projection standard error by Z=-2.58 (this being the lower 99.5th point of the N(0,1) distribution).

Stressed projection using Z=-2.58

The stressed-trend approach behind Figure 1 can be used for a variety of models - Table 1 shows the best-estimate and 99.5th percentile…

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Tags: longevity risk, Solvency II, model risk

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

Caveat emptor

(Apr 13, 2011)

I wrote earlier about survivor forwards as a means of transferring longevity risk.  One natural question for investors to ask is: what is the likelihood of loss exceeding a given amount?  The only sensible means of answering this question is to use a stochastic projection model - a deterministic model generates scenarios, but without attaching probabilities it cannot be used to approach this problem.

Consider an example where Party A (a pension scheme, say) offers a survivor forward based on males in England and Wales.  Party A offers to pay a fixed rate of 0.47 per £10 million nominal for survivors between age 60 and 85.  The investor, Party B, is asked to pay the floating leg, i.e. the actual survival rate, S. …

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Tags: survivor forward, S-forward, model risk, mortality improvements, mortality projections

Model risk

(Mar 14, 2011)

Investors in longevity risk are particularly interested in extremes - they want to know the maximum loss they are likely to bear for a given probability.  Reinsurers can be even more strongly interested in extremes, especially if they have written stop-loss reinsurance.  Regulators have the same interest - they want to know how well reserved the insurers and reinsurers are.

A major uncertainty in longevity risk is the path taken by future mortality improvements.  A common question under Solvency II in the EU is to ask what annuity reserves are required to be 99.5% sure that they are adequate.  To answer this, it is common to use a stochastic projection model as this gives a range of outcomes, each with an attaching…

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Tags: model risk, mortality improvements, mortality projections, Solvency II

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