# Mortality and Longevity Risk

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### Mortality and Longevity Risk

My work in this area began with 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 Andrew Cairns, David Blake and I have worked 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 …” or “A quantitative comparison …”) and age effects (see “CBDX – A workhorse mortality model” for the blog or “CBDX: A workhorse mortality model from the Cairns-Blake-Dowd family” for the full paper).

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 financial 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. I proposed survivor swaps (“Survivor Bonds: A Comment on Blake and Burrows”) in 2003 and we further examined the issues involved in survivor swaps in 2006 (Dowd, Blake, Cairns and Dawson, “Survivor swaps”). The ‘survivor’ terminology never took off, however – 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 grown to many billions in notional principal.
- The development of two-population mortality models (see, e.g., “A Gravity Model of Mortality Rates for Two Related Populations”), in which we model how mortality rates are related across different populations. These are potentially useful for the long-term hedging of longevity risks.
- Most recently, we have developed a new(ish) mortality model that uses an age effect to extend back into middle age, “CBDX – A workhorse mortality model” (2019).

#### Articles on Mortality Risk

“Built to Last: Analysing the Mortality Experiences of a Large Portfolio of Lives.” (AJG Cairns, D. Blake, K. Dowd, G. Coughlan, O. Jones and J. Rowney) *The Actuary* 2 November 2022.

“A General Framework for Analysing the Mortality Experience of a Large Portfolio of Lives: With an Application to the UK Universities Superannuation Scheme.” (A.G.J. Cairns, D. Blake, K. Dowd, G.D. Coughlan, O. Jones and J. Rowney). *European Actuarial* *Journal* *(*29 April 2022). https://doi.org/10.1007/s13385-022-00309-1.

**“Projecting Mortality Rates to Extreme Old Age with the CBDX Model.” **Dowd, K. and D. Blake (2022) *Forecasting* 4, 208-218. https://doi.org 10.3390/forecast4010012

“CBDX: A Workhorse Mortality Model from the Cairns-Blake-Dowd Family” (K. Dowd, A.J.G. Cairns and D. Blake) *Annals of Actuarial Statistics*, 2020 1–16. https://doi.org/10.1017/S1748499520000159.

“Hedging Pension Risks with the Age-Period-Cohort Two-Population Gravity Model.” (K. Dowd, A.J.G. Cairns and D. Blake) *North American Actuarial Journal*. Published online on 20 November 2019 at https://www.tandfonline.com/doi/full/10.1080/10920277.2019.1652102.

“On the Projection of Mortality Rates to Extreme Old Age.” (K. Dowd and D. Blake) Pensions Institute Discussion Paper PI – 1909 (30 July 2019).

“A Simple Approach to Projecting Extreme Old Age Mortality Rates and Value Mortality-Related Financial Instruments.” (K. Dowd, A.J.G. Cairns and D. Blake) Institute Discussion Paper PI – 1907 (11 May 2019).

“Modelling Socio-Economic Differences in the Mortality of Danish Males Using a New Affluence Index.” (A.J.G. Cairns, M. Kallestrup-Lamb, C.P.T. Rosenskjold, D. Blake and K. Dowd) *ASTIN Bulletin* (2019) 49: 555-590.

“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,* 2010, Vol. 48, pp. 355-367.

“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.

“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.

“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.

“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. 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

“Still Living with Mortality: the Longevity Risk Transfer Market After One Decade.” (D. Blake, A.J.G. Cairns, K. Dowd and A.R. Kessler) Presented at a Sessional Research Meeting of the Institute and Faculty of Actuaries, 29 January 2018. *British Actuarial Journal* 24: 1-80.

“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.

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

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

**Other Articles on Mortality and Longevity Risk**

“Built to Last: Analysing the Mortality Experiences of a Large Portfolio of Lives.” (AJG Cairns, D. Blake, K. Dowd, G. Coughlan, O. Jones and J. Rowney) *The Actuary* 2 November 2022.

“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 Financial Risk Measures.” (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.