Stephen Richards

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Articles written by Stephen Richards

What — and when — is a 1:200 event?

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.

12 November 2015 Tags: Spanish influenza pandemic, mortality shocks, longevity shocks, Solvency II, ICA, SST, VaR, value-at-risk

Reviewing forecasts

When making projections and forecasts, it can be instructive to compare them with what actually happened. In December 2002 the CMI published projections of mortality improvements that incorporated the so-called "cohort effect" (CMIB, 2002). These projections were in use by life offices and pension schemes in the United Kingdom from 2003 onwards.

19 October 2015 Tags: cohort effect, mortality projections, mortality improvements

Can I interest you in a guaranteed loss-making investment?

Would you buy an investment which was guaranteed to lose you money?

30 January 2015 Tags: yield curve, interest rate, Strafzinsen

Conditional tail expectations

In a recent posting I looked at the calculation of percentiles and quantiles, which underpin many calculations for ICA and Solvency II. Simply put, an $\alpha$-quantile is the value which is not expected to be exceeded $\alpha\times 100$% of the time. This value is denoted $Q_{\alpha}$. Mathematically, for a continuous random variable, $X$, and a given probability level $\alpha$ we have:

$$\Pr(X\leq Q_\alpha)=\alpha$$

10 October 2014 Tags: conditional tail expectation, quantile, percentile, coherence, subadditivity

Don't cut corners

An important class of mortality-projection models is the Cairns-Blake-Dowd (CBD) family.

07 October 2014 Tags: cohort effect, Cairns-Blake-Dowd, M6 model, M7 model

Quantiles and percentiles

Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. They are generally described as q-quantiles, where q specifies the number of intervals which are separated by q−1 points.

20 August 2014 Tags: quantile, percentile, Solvency II, Excel, R language

Creative thinking around longevity risk

The U.K. has been a hotbed of innovation when dealing with the longevity risk found in pension schemes.

06 July 2014 Tags: longevity risk, regulation, longevity swaps

Excel's limits

We have written in the past about some of the reasons why we don't use Excel to fit our models. However, we do use Excel for validation purposes — fitting models using two entirely separate tools is a good way of checking production code. That said, there are some important limits to Excel, especially when it comes to fitting projection models.

27 June 2014 Tags: Excel, Lee-Carter, APC, Cairns-Blake-Dowd

(Un)Fit for purpose

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.

26 May 2014 Tags: Lee-Carter, Renshaw-Haberman, model risk

A second pension-scheme revolution

In his book Unseen Revolution, Peter Drucker drew attention to the structural changes in economic ownership which were silently ushered in with the growth of corporate pension schemes.

20 March 2014 Tags: pension schemes, bulk annuities, buy-out