1. University of New South Wales
CICIRM 2013
Developments in Mortality and Longevity Risk Modeling
Michael Sherris
University of New South Wales
2013 China International Conference on Insurance And Risk Management (CICIRM 2013)
July 17th-20th, 2013
Expo Garden Hotel, Kunming, Yunnan ,China

2. Longevity/Mortality Models
Mortality/Longevity Models
Demographic and Actuarial models
Life tables
Improvement factors
Stochastic Survival Curve models
Aged based non-Parametric or Parametric survival curve
Stochastic parameters
Financial Risk Framework models
Risk factor dynamics
Price of risk
Consistent
Market calibration

3. Longevity/Mortality Models Data
Individuals
Risk factors: Age, sex, smoking status, education, occupation, ethnicity, income, geographical location, marital status
Cause of death
Survey data
Population by country
Aggregate mortality by age, gender, period, cohort
Aggregate health data
Prevalence of health conditions
Mortality rates by Causes of death
Life insurance, pension fund and annuity pools
Aggregation of deaths and exposures by underwriting risk factors
Effect of selection

4. Longevity/Mortality Model Risk
Systematic Risk
Uncertain future mortality – age-period-cohort trends, survival curve, risk factors, price of risk
Idiosyncratic Risk
Pooling of individual survival risks – pool size, assumption of i.i.d. risks
Heterogeneity
Mortality rates and trends varying by individuals of the same age (gender)

5. Agenda – Model Risks
Cohort and forward survival curves (financial risk) versus age-period models (demographic/actuarial/survival curve adapted for cohort effects)
Consistent versus inconsistent mortality curves (dynamics and future survival curves) and parameter stability
Risk factors and price of risk (explicit versus ad-hoc risk adjustment)
Heterogeneity – multiple state models with systematic risk versus heterogeneity only (frailty, Markov ageing models)
Drawing on longevity research at CEPAR, UNSW

6. Some of the issues – which would you prefer?
Model A
Model B
Males
Source: Shao, W., Sherris, M., and Hanewald, K., (2103), Reverse Mortgage Pricing and Capital Requirements Allowing for Idiosyncratic House Price Risk and Longevity Risk.

7. Some of the issues – which would you prefer?
Model A
Females
Model B
Source: Shao, W., Sherris, M., and Hanewald, K., (2103), Reverse Mortgage Pricing and Capital Requirements Allowing for Idiosyncratic House Price Risk and Longevity Risk.

8. Systematic Mortality Model Risk
Model A
Model B
Discrete age survival function
Cohort trends – period and age-to-age variability and trends
Cohort curve generated by the dynamics
Multiple risk factors based on age
Dependence in volatility –principal components
Parametric survival function - smoothing of age-to-age variability
Period trends
Cohort curve read off projected period curves
Two factors - stochastic parameters of mortality curve
Dependence – two factors, from smoothed curve dynamics

9. Importance of cohort and forward survival curves
Source: Alai, D.H. and Sherris, M. (2012), Rethinking Age-Period-Cohort Mortality Trend Models, Article published on line 16 Apr 2012, Scandinavian Actuarial Journal

10. Model Mortality Surface (age-period and cohort)
Source: C. Blackburn and M. Sherris, (2013), Consistent Dynamic Affine Mortality Models for Longevity Risk Applications, Insurance: Mathematics and Economics, Volume 53, Issue 1, July 2013, Pages 64–73

11. Quantification of Systematic Longevity Risk
Forward survival curves (cohort)
Expected survival curves and pricing
Source: C. Blackburn and M. Sherris, (2013), Consistent Dynamic Affine Mortality Models for Longevity Risk Applications, Insurance: Mathematics and Economics, Volume 53, Issue 1, July 2013, Pages 64–73

12. Consistent survival curves – 3 factor model
Three Factor Consistent HJM mortality model
Dynamics generates consistent survival curves
Source: C. Blackburn and M. Sherris, (2013), Consistent Dynamic Affine Mortality Models for Longevity Risk Applications, Insurance: Mathematics and Economics, Volume 53, Issue 1, July 2013, Pages 64–73

13. Consistent model risk factors – 3 factor estimation stability
Refitting model at different time points demonstrates model consistency
How many models used in practice have this property?
Source: C. Blackburn and M. Sherris, (2013), Consistent Dynamic Affine Mortality Models for Longevity Risk Applications, Insurance: Mathematics and Economics, Volume 53, Issue 1, July 2013, Pages 64–73

14. Consistent Survivor Curves – 2 versus 3 factor
Increase in number of factors explains older age mortality better
Source: C. Blackburn and M. Sherris, (2013), Consistent Dynamic Affine Mortality Models for Longevity Risk Applications, Insurance: Mathematics and Economics, Volume 53, Issue 1, July 2013, Pages 64–73

15. Best Estimate Forward Survivor Curve – 2 factors
Removes need for simulations in simulations for ALM, valuation, risk quantification

16. Price of Risk and Forward Survivor Curve – 2 factors

17. Price of risk – financial approaches versus actuarial (Wang transform)
Wang transform gives wrong signs and magnitude for prices of risk (offset by other parameters)
Sharpe ratio scales the survivor curve and does not impact risk factor loadings

18. Price of risk - longevity risk swap pricing
Pricing differences less pronounced than for risk quantification

19. Price of risk versus volatility parameter risk – survival curve
Source: Fung, M. C., Ignatieva, K. and Sherris, M., (2013), Systematic Mortality Risk: An Analysis of Guaranteed Lifetime Withdrawal Benefits in Variable Annuities

20. Price of risk versus volatility parameter risk - GLWB
Equity exposure
Mortality risk premium
Source: Fung, M. C., Ignatieva, K. and Sherris, M., (2013), Systematic Mortality Risk: An Analysis of Guaranteed Lifetime Withdrawal Benefits in Variable Annuities

21. Price of risk and impact on risk based capital
Solvency capital costs versus longevity swap for a life annuity
Varying price of risk in Model A
Incentives to hedge shorter terms and retain tail risk with higher prices of risk
Source: Meyricke, R. and Sherris, M. (2013), Optimal Longevity Risk Management Under Solvency II

22. Mortality heterogeneity - which model?
Calibration to population data versus individual data (GLMM)
Frailty versus Markov ageing
Does not include systematic mortality risk required to assess solvency/tail risk
Source: Ramona Meyricke and Michael Sherris (2013), The determinants of mortality heterogeneity and implications for pricing underwritten annuities.

23. Heterogeneity model risk – longevity tail risk for annuity fund
Fixed investment return of 3% p.a.
Mortality model
Heterogeneity
Annuity premium
Risk measures at age 110
Mean
Stdev
95% VaR
Markov
best health only
16.32
-0.07
386.09
631.73
mixed
14.29
-15.86
710.31
mixed w self selection
428.07
Le Bras
15.84
4.24
607.33
986.31
14.16
11.56
635.70
613.12
Vaupel
16.29
-0.88
658.73
14.72
-1.61
673.32
666.36
Effect of adverse selection
Premium for a life annuity of 1 p.a. and tail risk measures for a pool of 1000 individuals aged 65.
Source: Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk.

24. Heterogeneity model risk – investment and longevity tail risk for annuity fund
Random investment return
Mortality model
Heterogeneity
Annuity premium
Risk measures at age 110
Mean
Stdev
95% VaR
Markov
best health only
13.48
state 2
12.54
state 3
10.04
state 4
6.74
-54.63
state 5
5.00
-35.88
mixed
11.99
mixed w self selection
Le Bras
12.95
11.84
-59.61
Vaupel
13.14
12.13
Investment risk magnifies longevity risk and impact of selection
Premium for a life annuity of 1 p.a. and tail risk measures for a pool of 1000 individuals aged 65
Results are shown for the different deterministic models of heterogeneity.
Source: Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk.

25. Heterogeneity model risk – impact of systematic longevity risk
Pool size
Deterministic Markov
Subordinated Markov
100
122.66
286.21
1000
388.23
10000
100000
Standard deviation of the fund at age 110 for life annuity of 1 p.a. for best health individuals aged 65
Fixed investment return of 3% p.a.
Stochastic model variance of Gamma time change ν=0.095.
Source: Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk.

26. Summary – key points
Mortality/longevity risk model developments – key ideas
Model consistency and parameter stability
Tractability and ease of application
Risk factors and price of risk
Heterogeneity and data

27. Thank you for your attention
Michael Sherris
School of Risk and Actuarial Studies
ARC Centre of Excellence in Population Ageing Research
University of New South Wales
Acknowledgement: ARC Linkage Grant Project LP Managing Risk with Insurance and Superannuation as Individuals Age with industry partners PwC, APRA and the World Bank as well as the support of the Australian Research Council Centre of Excellence in Population Ageing Research project CE

28. References
Alai, D.H. and Sherris, M. (2012), Rethinking Age-Period-Cohort Mortality Trend Models, Article published on line 16 Apr 2012, Scandinavian Actuarial Journal, DOI: / Su, S. and Sherris, M. (2012), Heterogeneity of Australian Population Mortality and Implications for a Viable Life Annuity Market, Insurance: Mathematics and Economics, 51, 2, 322–332. Ziveyi, J, Blackburn, C., and Sherris, M. (2013), Pricing European Options on Deferred Annuities, Insurance: Mathematics and Economics, Volume 52, Issue 2, March 2013, 300–311. Blackburn, C. and Sherris, M., (2013), Consistent Dynamic Affine Mortality Models for Longevity Risk Applications, Insurance: Mathematics and Economics, Volume 53, Issue 1, July 2013, Pages 64–73 Meyricke, R. and Sherris, M. (2013), The determinants of mortality heterogeneity and implications for pricing underwritten annuities, accepted Insurance: Mathematics and Economics, on-line 29 June 2013; Meyricke, R. and Sherris, M. (2013), Optimal Longevity Risk Management Under Solvency II. Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk. Fung, M. C., Ignatieva, K. and Sherris, M., (2013), Systematic Mortality Risk: An Analysis of Guaranteed Lifetime Withdrawal Benefits in Variable Annuities. Shao, W., Sherris, M., and Hanewald, K., (2103), Reverse Mortgage Pricing and Capital Requirements Allowing for Idiosyncratic House Price Risk and Longevity Risk.