What — and when — is a 1:200 event?

(Nov 12, 2015)

The concept of a "one in two hundred" (1:200) event over a one-year time horizon is well established as a reserving standard for insurance in several territories: the ICA in the United Kingdom, the SST in Switzerland and the forthcoming Solvency II standard for the entire European Union.  The basic idea is simple: insurers must be capitalised to withstand 99.5% of events which could arise over the coming year.  Other territories use concepts like conditional tail expectations.

There is room for debate as to what constitutes a 1:200 event, however.  For example, Figure 1 shows the elevated mortality caused by the 1918 influenza pandemic, which for many people would be a starting point for calibrating a modern…

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Tags: Spanish influenza pandemic, mortality shocks, longevity shocks, Solvency II, ICA, SST, 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.


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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

Seminar on stochastic projection models

(Apr 16, 2012)

We previously ran a seminar on stochastic projection models for longevity risk. Our follow-up seminar focuses on specific aspects of ICAs and Solvency II.  The seminar contains four presentations:

  1. Improving the Lee-Carter model using smoothing techniques (Iain Currie).
  2. Issues with parameter correlations, illustrated by the APC model (Iain Currie).
  3. Testing the robustness of an internal model before committing to using it (Gavin Ritchie).
  4. A value-at-risk (VaR) framework for longevity trend risk (Stephen Richards).

The slide packs can be downloaded from the panel on the right.

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Tags: mortality projections, Solvency II, ICA

A head for tails

(Nov 19, 2011)

When an insurer or reinsurer takes on a new insurance risk, there are two things of special interest: the best estimate of the risk and the tail risk.  The best estimate is about the current expectation of claim levels or costs, while tail risk is about how bad things could get if the company were unlucky.  The UK's ICA regime and the pending EU Solvency II regime are both concerned with tail risk at the 99.5th percentile.

When investigating tail risk, we are talking about the right-hand tail of a loss distribution, i.e. the part which contains the rare-but-costly scenarios.  It is therefore critically important that the model used does a good job of estimating the size and shape of this tail.  Since the loss is a random…

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Tags: tail risk, Solvency II, ICA

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

The cost of uncertainty

(Mar 10, 2010)

In an earlier blog I wrote about how stochastic volatility in run-off increases with age. This applies when you exactly know (or think you know) the current and future mortality rates.

Of course, in practice we are not certain about current or future rates.  What impact does this have?  A good way of exploring this is to use a stochastic projection model.  Table 1 shows the annuity factors at key ages using a best-estimate projection and a typical ICA or Solvency II stress test (50th and 99.5th percentiles, respectively).

Table 1. Annuity factors and relative capital increase for level annuity when moving from 50th to 99.5th percentile. ONS data for mortality of males in England & Wales, P-spline age-period…

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Tags: mortality projections, ICA, Solvency II, matching

Getting used to Solvency II

(Mar 2, 2010)

Insurers and reinsurers throughout the EU are facing up to the implementation of Solvency II, a radical overhaul of regulatory standards for insurance business.  Recently we explored how much Solvency II demands stochastic models.  Another feature of Solvency II is the so-called "use test", which has been described as follows:

"Are the insurance firm's internal risk measurement systems closely integrated into its day-to-day risk management processes? [...] Put simply, the "use test" refers to the need for the risk-measurement judgements to play a key role in the management of a firm before they will be accepted also for regulatory purposes."

Source: John Tiner, then…

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Tags: Solvency II, use test, ICA

Does Solvency II demand stochastic models?

(Jan 24, 2010)

Solvency II is a major overhaul of the reserving rules for insurers throughout the European Union.  An important consideration for annuity writers is how it will relate to longevity trend risk.  For example, consider the following text about "Statistical quality standards" as they refer to insurers' internal models:

"The methods used to calculate the probability distribution forecast shall be based on adequate, applicable and relevant actuarial and statistical techniques and shall be consistent with the methods used to calculate technical provisions. The methods used to calculate the probability distribution forecast shall be based upon current and credible information and realistic…

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Tags: longevity risk, Solvency II, ICA

Over-dispersion (reprise for actuaries)

(Jan 3, 2010)

In my previous post I illustrated the effects of over-dispersion in population data.  Of course, an actuary could quite properly ask: why use ONS data?  The CMI data set on assured lives might be felt to be a better guide to the mortality of pensioners, although Stephen has raised a question mark over this assumption in the past.

Figure 1 illustrates what happens with the CMI data set. The over-dispersion parameter is much smaller at 1.82, so the Poisson model gives a reasonable forecast.  Note that the over-dispersion in the CMI data comes from a different source, namely the presence of duplicates causing extra variability in death counts.  However, the same approach to over-dispersion works regardless of the…

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Tags: over-dispersion, duplicates, mortality projections, ICA, Solvency II

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