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

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

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

Benchmarking VaR for longevity trend risk

(Mar 1, 2013)

I recently wrote about an objective approach to setting the value-at-risk capital for longevity trend risk.  This approach is documented in Richards, Currie & Ritchie (2012), which was recently presented to a meeting of actuaries in Edinburgh.  One of the topics which came up during the discussion was how the answers from the value-at-risk (VaR) method squared with how life offices actually change their projection bases in practice.  In particular, commentators were interested in what might be regarded as a "real world" example of a sudden change in projection basis, and how this might compare with the results from the VaR framework.

As it happens, we do have an historical example to call upon, and furthermore…

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Tags: mortality improvements, mortality projections, VaR, CMI, value-at-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

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

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