Mortality and longevity risk

My work in this area began after Andrew Cairns became interested in mortality modelling. This led to the Cairns-Blake-Dowd (CBD) mortality model (2006) which rapidly became adopted as one of the standard models in the area (“A two factor model ...”). Since then we have been working on various extensions to the original CBD model, mainly to incorporate the impact of cohort or year-of-birth effects (see, e.g., “Modelling and management of mortality risk ...” and “A quantitative comparison ...).

 

An introduction/overview of the CBD model and its various extensions can be found in the CBD Model homepage. This homepage includes a page about the model, a demo and downloadable Excel workbook that allows the user to estimate the model’s parameters.

 

Within the mortality/longevity area, I have been involved mainly in the following topics:

  • The estimation of mortality-related measures of financial risk: see “Mortality-dependent risk measures”.
  • The creation of mortality and mortality-related fan charts. The former would involve fan charts of prospective mortality rates over time, and the latter would involve fan charts for future survivorship rates, expected longevity and future annuity prices. 
  • The backtesting of mortality projections, i.e., assessing how past projections have fared in the light of subsequently realised mortality outcomes (see “Backtesting stochastic mortality models ....”).
  • Financial derivatives based on mortality-related underlying variables.  Such derivatives were first proposed by David Blake in 1999 when he advocated the issue of survivor bonds (see Blake and Burrows “Survivor bonds”), and interest in them grew thereafter. We then examined the issues involved in survivor swaps in 2006 (See Dowd, Blake, Cairns and Dawson, “Survivor swaps”). (Along with a paper by Lin and Cox (Cox, Samuel H. and Yijia Lin (2007) “Natural Hedging of Life and Annuity Mortality Risks”, North American Actuarial Journal 11(3), 1-15), this was I believe the first paper on this subject.) The ‘survivor’ terminology never took off - most people now refer to longevity bonds and longevity swaps instead - but the market in longevity swaps did, and the longevity swaps market in London has already grown to billions in notional principal. One can only hope that longevity derivatives don’t go the way that credit derivatives did ....
  • Most recently, the development of two-population mortality models, in which we model how mortality rates are related across different populations. These are potentially useful for the long-term hedging of longevity risks.  

 

Articles on mortality risk and mortality-related fan charts

 

“Phantoms Never Die: Living with Unreliable Population Data,” (A. J. G. Cairns, D. Blake, K. Dowd and A.R. Kessler) Journal of the Royal Statistical Society, Series A, Vol. 179, 2016, pp.

975-1005.

 

“Le Nouveau Marché du Risque de Longevité.” (D. Blake, A.J.G.Cairns, G.D. Coughlan, K. Dowd and R. MacMinn) Revue d’Economie Financiere, Juin 2016, No. 122, pp. 129-164.

 

“The Myth of Methusalah and the Uncertainty of Death: The Mortality Fan Charts.” (K. Dowd, D. Blake and A.J.G. Cairns) Risks 4, 21, May 2016, pp. 1-7.

 

“Longevity Risk Effectiveness: A Decomposition.”  (A. J. G. Cairns, K. Dowd, D. Blake and G. D. Coughlan), Quantitative Finance, Volume 14, No. 2, 2014, pp. 217-235.

“Longevity Risk and Hedging Solutions.” (G. Coughlan, D. Blake, R. MacMinn, A.J.G. Cairns and K. Dowd). Pp. 97-1035 in G. Dionne (ed.) Handbook of Insurance. New York: Springer, 2013.

“The New Life Market.” (D. Blake, A. Cairns, G. Coughlan, K. Dowd and R. MacMinn) Journal of Risk and Insurance, 2013, pp. 1-57. Published online, July 1 2013.

Bayesian Stochastic Mortality Modelling for Two Populations.” (A. J. G. Cairns, D. Blake, K. Dowd, G. D. Coughlan, and M. Khalaf-Allah) ASTIN Bulletin, Vol. 41, Number 1, pp. 29-59.

Longevity Hedging 101: A Framework for the Longevity Basis Risk Analysis and Hedge Effectiveness.” (G. D. Coughlan , M. Khalaf-Allah, Y. Ye, S. Kumar, A. J. G. Cairns, D. Blake and K. Dowd) North American Actuarial Journal, 2011, Vol. 15, No. 2, pp. 150-176.

A Gravity Model of Mortality Rates for Two Related Populations”. (K. Dowd, A. J.G. Cairns, D. Blake, G. D. Coughlan, D. Epstein, and M. Khalaf-Allah) North American Actuarial Journal, 2011, Vol. 15, No. 2, pp.

Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models.” (A. J.G. Cairns, D. Blake, K. Dowd, G. D. Coughlan, and M. Khalaf-Allah) Insurance: Mathematics and Economics, Vol. 48, pp. 355-367.

Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of Multi-Period-Ahead Density Forecasts.”(K. Dowd, A. J. G. Cairns, D. Blake, G. D. Coughlan, D. Epstein and M. Khalaf-Allah) North American Actuarial Journal, 2010, Vol. 14, No. 4, pp. 281-298.

Evaluating the Goodness of Fit of Stochastic Mortality Models.” (K. Dowd, A. J. G. Cairns, D. Blake, G. D. Coughlan, D. Epstein and M. Khalaf-Allah) Insurance: Mathematics and Economics, 2010, Vol. 47, pp. 255-265.

Facing up to Uncertain Life Expectancy: the Longevity Fan Charts.” (K. Dowd, D. Blake and A. J. G. Cairns) Demography, Volume 47, Number 1, February 2010, pp. 67-78.

Survivor Derivatives: A Consistent Pricing Framework.” (P. Dawson, K. Dowd, A. J. G. Cairns and D. Blake) Journal of Risk and Insurance, 2009, Vol. 77, Issue No. 3, pp. 579–596.

A Quantitative Comparison of Stochastic Mortality Models Using Data from England & Wales and the United States.” (A. J. G. Cairns, D. Blake, K. Dowd, G. D. Coughlan, D. Epstein, A. Ong, and I. Balevich) North American Actuarial Journal, Volume 13, 2009, No. 1, pp. 1-35. [This article won the prize for the best paper in the NAAJ for 2009.]

Modelling and Management of Mortality Risk: A Review.” (A. J. G. Cairns, D. Blake and K. Dowd) Scandinavian Actuarial Journal,  Volume 108, 2008, No. 2, pp. 79-113.

Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models.” (A. J. G. Cairns, D. Blake, K. Dowd, G. D. Coughlan, D. Epstein and M. Khalaf-Allah) Pensions Institute Discussion Paper PI-0801, April 2008.

Longevity Risk and the Grim Reaper’s Toxic Tail: The Survivor Fan Charts.” (D. Blake, K. Dowd, and A.  J. G. Cairns), Insurance: Mathematics and Economics, Volume 42, 2008, pages 1062-1068.

A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration.” (A. J. G. Cairns, D. Blake and K. Dowd) Journal of Risk and Insurance. Volume 73, No. 4, December 2006, pp. 687-718. This paper set out the Cairns-Blake-Dowd (CBD or M5) mortality model which is now an industry-standard. This paper also won the American Risk and Insurance Association's Robert I. Mehr Award for the paper published ten years ago in The Journal of Risk and Insurance that has best stood the test of time, and is one of the major international awards in the field of risk and insurance.

Articles on mortality/longevity/survivor derivatives and related topics

Options on Normal Underlyings with an Application to the Pricing of Survivor Swaptions.” (P. Dawson, K. Dowd, A. J. G. Cairns and D. Blake). Journal of Futures Markets, 2009, Vo. 29, pp. 757-774.

The Birth of the Life Market.” (D. Blake, A. J. G. Cairns and K. Dowd) Asia-Pacific Journal of Risk and Insurance, Volume 3, 2008, Number 1, pages 6-36. Reprinted in Alternative Investment Quarterly, Issue 29, Fourth Quarter issue, pp. 9-30.

“Securitization/Life.” (Blake, D., and K. Dowd) Pp. 1623-1627 in E. Melnick and B. Everitt (eds) Encyclopedia of Quantitative Risk Assessment and Analysis. Chichester: John Wiley and Sons, 2008.

Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities.” (D. Blake, A. J. G. Cairns and K. Dowd) British Actuarial Journal, Volume 12, 2006, pp. 153-197. This paper won the Faculty of Actuaries in Scotland Prize for the best paper in the 2005-2006 session and was cited as “highly commended” by the Institute of Actuaries of England and Wales.

Longevity Bonds: Financial Engineering, Valuation and Hedging.” (D. Blake, A. J. G. Cairns, K. Dowd, and R. MacMinn) Journal of Risk and Insurance, Volume 73, No. 4, December 2006, pp. 647-672.

Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk.” (A. J. G. Cairns, D. Blake and K. Dowd) ASTIN Bulletin. Volume 36, Number 1, 2006, pp.79-120. This paper won the Bob Alting Von Geusau Prize for the best paper on financial risk published in the ASTIN Bulletin in 2005 and 2006, and the David Garrick Halmstad Prize 2006 awarded by the Actuarial Foundation for the best paper published in Actuarial Science in 2006.

Survivor Swaps.” (K. Dowd, D. Blake, A. J. G. Cairns and P. E. Dawson) Journal of Risk and Insurance. Volume 73, No. 1, March 2006, pp. 1-17.

Pricing Risk on Longevity Bonds.” (A. J. G. Cairns, D. Blake, P. E. Dawson and K. Dowd) Life and Pensions, Volume 1, No. 2 (November 2005), pp. 41-44.

“UK: The Benefits of Longevity Bonds.” (D. Blake, A. J. G. Cairns, S. H. Cox, P. E. Dawson, K. Dowd and R. MacMinn) Pensions International, February 2005, Issue Number 67, pp. 6-7.

“Pricing Frameworks for Securitization of Mortality Risk.” (A. J. G. Cairns, D. Blake and K. Dowd) Pp. 509-540 in Proceedings of the 14th International AFIR Colloquium, Boston. 2004.

“Survivor Bonds: A Comment on Blake and Burrows.” Journal of Risk and Insurance, 2003, Vol. 70, No. 2, pp. 339-348. 

Other articles on mortality and longevity

 

“Longevity and Risk Hedging Solutions” (G. D. Coughlan, D. Blake, R. MacMinn, A. J. G. Cairns and K. Dowd). Prepared for: Handbook of Insurance, Second Edition, Kluwer Academic Publishing, Edited by Georges Dionne.

Mortality-Dependent Measures of Financial Risk.” (K. Dowd, A. J. G. Cairns and D. Blake) Insurance: Mathematics and Economics, Vol. 38, 2006, pp. 427-440.

“The Grave Problem of Longevity Risk.” (K. Dowd, D. Blake and A. J. G. Cairns) Financial Engineering News, No. 49, May-June 2006, pp. 19, 30.