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transcript
Developments in Mortality and Longevity Risk Modeling
Michael SherrisUniversity of New South Wales
2013 China International Conference on Insurance And Risk Management (CICIRM 2013)
July 17th-20th, 2013Expo Garden Hotel, Kunming, Yunnan ,China
CICIRM 2013
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
Model A Model B
Some of the issues – which would you prefer?
Source: Shao, W., Sherris, M., and Hanewald, K., (2103), Reverse Mortgage Pricing and Capital Requirements Allowing for Idiosyncratic House Price Risk and Longevity Risk.
Males
Model A Model B
Some of the issues – which would you prefer?
Source: Shao, W., Sherris, M., and Hanewald, K., (2103), Reverse Mortgage Pricing and Capital Requirements Allowing for Idiosyncratic House Price Risk and Longevity Risk.
Females
Model A
• 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
Model B
• 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
Systematic Mortality Model Risk
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
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
Quantification of Systematic Longevity Risk
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
Forward survival curves (cohort)
Expected survival curves and pricing
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
Consistent model risk factors – 3 factor estimation stability
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
Refitting model at different time points demonstrates model consistency
How many models used in practice have this property?
Consistent Survivor Curves – 2 versus 3 factor
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
Increase in number of factors explains older age mortality better
Best Estimate Forward Survivor Curve – 2 factors
Removes need for simulations in simulations for ALM, valuation, risk quantification
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
Price of risk - longevity risk swap pricing
Pricing differences less pronounced than for risk quantification
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
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
Price of risk versus volatility parameter risk - GLWB
Price of risk and impact on risk based capital
Source: Meyricke, R. and Sherris, M. (2013), Optimal Longevity Risk Management Under Solvency II
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
Mortality heterogeneity - which model?
Source: Ramona Meyricke and Michael Sherris (2013), The determinants of mortality heterogeneity and implications for pricing underwritten annuities.
Calibration to population data versus individual data (GLMM)
Frailty versus Markov ageing
Does not include systematic mortality risk required to assess solvency/tail risk
Heterogeneity model risk – longevity tail risk for annuity fund
Mortality model HeterogeneityAnnuity premium
Risk measures at age 110
Mean Stdev 95% VaR
Markov
best health only 16.32 -0.07 386.09 631.73mixed 14.29 -15.86 710.31 1176.89mixed w self selection 14.29
-5872.49 428.07 6566.69
Le Bras
best health only 15.84 4.24 607.33 986.31mixed 14.16 11.56 635.70 1022.46mixed w self selection 14.16
-3105.13 613.12 4109.81
Vaupel
best health only 16.29 -0.88 658.73 1072.07mixed 14.72 -1.61 673.32 1109.78mixed w self selection 14.72
-2610.51 666.36 3694.48
Premium for a life annuity of 1 p.a. and tail risk measures for a pool of 1000 individuals aged 65.
Fixed investment return of 3% p.a.
Effect of adverse selection
Source: Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk.
Mortality model
Heterogeneity
Annuity premium
Risk measures at age 110
Mean Stdev 95% VaR
Markov
best health only 13.48 -199.80 4912.11 7843.93state 2 12.54 -198.90 4387.30 7117.17state 3 10.04 -111.25 3192.87 5144.76state 4 6.74 -54.63 1917.96 3131.44state 5 5.00 -35.88 1478.46 2441.54mixed 11.99 -132.34 4420.42 7051.55mixed w self selection 11.99 -14675.61 4112.85 21204.18
Le Bras
best health only 12.95 -109.05 4901.30 7811.46mixed 11.84 -59.61 4283.44 6883.19mixed w self selection 11.84 -7006.90 4244.59 13922.83
Vaupel
best health only 13.14 -141.61 5040.23 8067.82mixed 12.13 -112.90 4476.47 7234.56mixed w self selection 12.13 -5777.86 4397.70 12874.70
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.
Random investment return
Investment risk magnifies longevity risk and impact of selection
Source: Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk.
Heterogeneity model risk – investment and longevity tail risk for annuity fund
Pool size
Deterministic Markov
Subordinated Markov
100 122.66 286.211000 388.23 2588.74
10000 1216.31 25649.07100000 3914.59 254307.38
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.
Heterogeneity model risk – impact of systematic longevity risk
Source: Sherris, M. and Zhou, Q. (2013), Model Risk, Mortality Heterogeneity and Implications for Solvency and Tail Risk.
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
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Thank you for your attention
Michael Sherris m.sherris@unsw.edu.au
School of Risk and Actuarial StudiesARC Centre of Excellence in Population Ageing Research
University of New South Wales
Acknowledgement: ARC Linkage Grant Project LP0883398 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 CE110001029.
ReferencesAlai, D.H. and Sherris, M. (2012), Rethinking Age-Period-Cohort Mortality Trend Models, Article
published on line 16 Apr 2012, Scandinavian Actuarial Journal, DOI: 10.1080/03461238.2012.676563
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 http://dx.doi.org/10.1016/j.insmatheco.2013.04.007
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; http://www.sciencedirect.com/science/article/pii/S0167668713000887
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.