Skip to main content Accessibility help
×
Home
Hostname: page-component-684bc48f8b-g7stk Total loading time: 4.898 Render date: 2021-04-11T05:39:36.333Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Longevity trend risk over limited time horizons

Published online by Cambridge University Press:  21 May 2020

Stephen J. Richards
Affiliation:
Longevitas Ltd, 24a Ainslie Place, EdinburghEH3 6AJ, UK
Iain D. Currie
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EdinburghEH14 4AS, UK
Torsten Kleinow
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EdinburghEH14 4AS, UK
Gavin P. Ritchie
Affiliation:
Longevitas Ltd, 24a Ainslie Place, EdinburghEH3 6AJ, UK
Corresponding
E-mail address:

Abstract

We consider various aspects of longevity trend risk viewed through the prism of a finite time window. We show the broad equivalence of value-at-risk (VaR) capital requirements at a p-value of 99.5% to conditional tail expectations (CTEs) at 99%. We also show how deferred annuities have higher risk, which can require double the solvency capital of equivalently aged immediate anuities. However, results vary considerably with the choice of model and so longevity trend-risk capital can only be determined through consideration of multiple models to inform actuarial judgement. This model risk is even starker when trying to value longevity derivatives. We briefly discuss the importance of using smoothed models and describe two methods to considerably shorten VaR and CTE run times.

Type
Paper
Copyright
© Institute and Faculty of Actuaries 2020

Access options

Get access to the full version of this content by using one of the access options below.

References

Akaike, H. (1987). Factor analysis and AIC. Psychometrica, 52, 317–333. ISSN 0033–3123. doi: https://doi.org/10.1007/BF02294359.CrossRefGoogle Scholar
Bank of England Prudential Regulatory Authority. Solvency II: internal model and matching adjustment update. Letter to UK-regulated insurers and reinsurers, March 2015. http://www.bankofengland.co.uk/pra/Pages/publications/ps/2016/ps3316.aspx.Google Scholar
Blake, D., Cairns, A.J.G., Dowd, K. & Kessler, A.R. (2018). Still living with mortality: the longevity risk transfer market after one decade. British Actuarial Journal, 24, e1. doi: https://doi.org/10.1017/S1357321718000314.Google Scholar
Boumezoued, A. (2020) Improving HMD mortality estimates with HFD fertility data. North American Actuarial Journal, 125.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687718. doi: https://doi.org/10.1111/j.1539-6975.2006.00195.x.CrossRefGoogle Scholar
Cairns, A.J.G. & El Boukfaoui, G. (2019) Basis risk in index based longevity hedges: a guide for longevity hedgers. North American Actuarial Journal, 122.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. & Khalaf-Allah, M. (2011). Mortality density forecasts: an analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48, 355367.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K. & Kessler, A. (2015). Phantoms never die: living with unreliable mortality data. Journal of the Royal Statistical Society, Series A. doi: https://doi.org/10.1111/rssa.12159.Google Scholar
Currie, I.D. (2011). Modelling and forecasting the mortality of the very old. ASTIN Bulletin, 41, 419427. doi: 10.2143/AST.41.2.2136983.Google Scholar
Currie, I.D. (2013). Smoothing constrained generalized linear models with an application to the Lee-Carter model. Statistical Modelling, 13(1), 6993. doi: https://doi.org/10.1177%2F1471082X12471373CrossRefGoogle Scholar
Currie, I.D. (2020). Constraints, the identifiability problem and the forecasting of mortality. Annals of Actuarial Science, 130CrossRefGoogle Scholar
Currie, I.D., Durban, M. & Eilers, P.H. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279298. doi: https://doi.org/10.1191%2F1471082X04st080oaCrossRefGoogle Scholar
Delwarde, A., Denuit, M. & Eilers, P.H.C. (2007). Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: a penalized likelihood approach. Statistical Modelling, 7, 2948. doi: https://doi.org/10.1177%2F1471082X0600700103CrossRefGoogle Scholar
Eilers, P.H.C. & Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89121. ISSN 08834237. http://www.jstor.org/stable/2246049.CrossRefGoogle Scholar
Hardy, M.R. (2006). An introduction to risk measures for actuarial applications. Casualty Actuarial Society.Google Scholar
Harrell, F.E. & Davis, C.E. (1982). A new distribution-free quantile estimator. Biometrika, 69, 635640. ISSN 00063444. doi: https://doi.org/10.1093/biomet/69.3.635. http://www.jstor.org/stable/2335999.CrossRefGoogle Scholar
Hyndman, R. (2013). Bug 15396 – Initialization of regression coefficients in arima(). https://bugs.r-project.org/bugzilla/show_bug.cgi?id=15396 .Google Scholar
Kleinow, T. & Richards, S.J. (2016). Parameter risk in time-series mortality forecasts. Scandinavian Actuarial Journal, 2016(10), 125. doi: https://doi.org/10.1080/03461238.2016.1255655.Google Scholar
Langou, J. (2010). Lapack 3.2.2 release notes. http://www.netlib.org/lapack/lapack-3.2.2.html.Google Scholar
Lee, R.D. & Carter, L. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659671. ISSN 01621459. http://www.jstor.org/stable/2290201.Google Scholar
Liu, Y. & Li, J.S.-H. (in press). An efficient method for mitigating longevity value-at-risk. North American Actuarial Journal, Special Issue for the 13th International Longevity Risk and Capital Markets Solutions Conference.Google Scholar
Macdonald, A.S., Richards, S.J. & Currie, I.D. (2018). Modelling Mortality with Actuarial Applications. Cambridge University Press. ISBN 978-1-107-04541-5.CrossRefGoogle Scholar
R Core, Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.Google Scholar
Renshaw, A.E. & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556570.Google Scholar
Richards, S.J. & Currie, I.D. (2009). Longevity risk and annuity pricing with the Lee-Carter model. British Actuarial Journal, 15(II) No. 65, 317365 (with discussion). doi: https://doi.org/10.1017/S1357321700005675.CrossRefGoogle Scholar
Richards, S.J., Currie, I.D., Kleinow, T. & Ritchie, G.P. (2019). A stochastic implementation of the APCI model for mortality projections. British Actuarial Journal, 24, e13. doi: 10.1017/S1357321718000260. https://www.longevitas.co.uk/apci.CrossRefGoogle Scholar
Richards, S.J., Currie, I.D. & Ritchie, G.P. (2014). A value-at-risk framework for longevity trend risk. British Actuarial Journal, 19(1), 116167. doi: https://doi.org/10.1017/S1357321712000451. https://www.longevitas.co.uk/var.CrossRefGoogle Scholar
Richards, S.J., Kirkby, J.G. & Currie, I.D. (2006). The importance of year of birth in two-dimensional mortality data. British Actuarial Journal, 12(I), 561 (with discussion). doi: https://doi.org/10.1017/S1357321700004682.CrossRefGoogle Scholar
Wilmoth, J.R., Andreev, K., Jdanov, D., Glei, D.A. & Riffe, T. (2017). Methods Protocol for the Human Mortality Database. https://www.mortality.org/Public/Docs/MethodsProtocol.pdf.Google Scholar
Woods, S. (2016). Reflections on the 2015 Solvency II internal model approval process. Bank of England Prudential Regulation Authority. http://www.bankofengland.co.uk/pra/Pages/publications/ps/2016/ps3316.aspx.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 9
Total number of PDF views: 63 *
View data table for this chart

* Views captured on Cambridge Core between 21st May 2020 - 11th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Longevity trend risk over limited time horizons
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Longevity trend risk over limited time horizons
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Longevity trend risk over limited time horizons
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *