Product Pricing and Solvency Capital Requirements for Long-Term Care Insurance

Product Pricing and Solvency Capital Requirements for Long-Term Care Insurance Adam W. Shao, Michael Sherris, Joelle H. Fong ARC Centre of Excellence in Population Ageing Research (CEPAR) UNSW Australia 23 rd Annual Colloquium of Superannuation Researchers 6-7 July 2015, Sydney

1/29 Topic Coverage 1 Introduction 2 Methodology Health Dynamics Base Products: Thiele's Dierent Equation Products with Typical Feature: Simulation-Based Approach Solvency Capital Requirements 3 Results Demographic Characteristics Premiums Reserves Solvency Capital Requirements 4 Conclusions

2/29 Topic coverage 1 Introduction 2 Methodology Health Dynamics Base Products: Thiele's Dierent Equation Products with Typical Feature: Simulation-Based Approach Solvency Capital Requirements 3 Results Demographic Characteristics Premiums Reserves Solvency Capital Requirements 4 Conclusions

2/29 Background - LTC Costs and Funding LTC costs are increasingly higher and the increasing trend is projected to continue (Congressional Budget Oce, 2004; Shi and Zhang, 2013; Productivity Commission of Australia, 2013) LTC costs funding scheme Australia: lifetime stop-loss mechanism U.S.: Medicaid and Medicare + private insurance + personal payment The private LTC insurance market is an important supplement for the public funding source (Productivity Commission of Australia, 2011; Glendinning et al., 2004; Colombo et al., 2011)

3/29 Background - LTC Insurance Pays benets when the insured becomes functionally disabled Based on number of Activities of Daily Livings (ADLs) that individuals cannot perform independently and cognitive impairment Six ADLs in the U.S. Health and Retirement Studies data: dressing, walking, bathing, eating, transferring in/out of bed, and toileting Typically two or three out of six ADLs Australian Bureau of Statistics data: Core Activity Restrictions Five ADLs in Australian Institute of Health and Welfare (AIHW) data: self-care, movement activities, moving around places, communication, and health-care tasks.

4/29 Types of LTC Insurance Four dierent types based on benets Fixed benet policies sold to healthy individuals Fixed benet policies sold to the elderly entering or already staying in long-term care facilities Indemnity-based benet policies Policies that allow the insured to choose between xed benet and long-term care service Can also be categorised into: Base policies With an elimination period (3 months to 2 years) and a maximum benet period (3 to 5 years)

5/29 Fixed Benet LTC Insurance Most typical and widely used is the xed benet policy Stand-alone policies Included as a rider benet in whole life insurance xed death benet draw-down death benet Life care annuities long-term care insurance combined with life annuity reduces adverse selection by pooling longevity risk and disability risk potential for reduced LTC insurance premiums

6/29 Research Questions This paper Derives premiums and best-estimate reserves for a broad range of xed benet LTC insurance policies Calculates solvency capital requirements for product providers Investigates the eectiveness of typical product features, such as the elimination period and the maximum benet period Investigates capital requirements for dierent types of products sold to dierent cohorts

7/29 Topic coverage 1 Introduction 2 Methodology Health Dynamics Base Products: Thiele's Dierent Equation Products with Typical Feature: Simulation-Based Approach Solvency Capital Requirements 3 Results Demographic Characteristics Premiums Reserves Solvency Capital Requirements 4 Conclusions

Markov Model Framework M H S D Figure. Four-state Markov transition diagram. 7/29 H - Healthy, diculty in no ADLs M - Mildly disabled, diculty in 1-2 ADLs S - Severely disabled, diculty in 3-6 ADLs D - Dead

8/29 Notation Ω χ = {H, M, S, D}: State space x: Age last birthday χ(x) Ω χ : Health state at age x Transition probability: For i, j Ω χ p ij (x, x + t) = Pr {χ(x + t) = j χ(x) = i} Transition intensity: For i, j Ω χ and i j µ ij (x) = lim x 0 + p ij (x, x + x) x µ ij (x): graduated using GLMs based on HRS data (Fong et al., 2013)

9/29 Data Health and Retirement Study (HRS) data: nationally representative survey of Americans over the age of 50 12-year observation with 7 biannual waves, 1998-2010 Longitudinal data on self-responded health status: ADLs and CI Cognition is evaluated by episodic memory and mental status: 7- out of 35 points is CI Sample: 19,547 individuals (56.5% females) without considering CI Sample: 18,781 individuals (57.4% females) respond to cognition scores

10/29 Thiele's Dierential Equation dv i (t, T ) dt = δv i (t, T ) b i (t) j i ( ) µ ij (x +t) B ij (t)+v j (t, T ) V i (t, T ) i, j Ω χ = {H, M, S, D} V i (t, T ): time t expected present value of benets paid to an individual in state i within the period (t, T ) δ: the continuously compounded interest rate b i (t): the annuity payment to the insured while in state i at time t (sojourn benet) B ij (t): the benet payment upon transitions from state i to state j at time t (transition benet) V D (t, T ) 0

11/29 Simulation-Based Approach Products with exible features: Benets depend on durations in one or multiple states Benets are not Markovian Hard to use Thiele's dierential equation Simulation-based approach Simulate health paths for 40,000 males and 40,000 females Benets depend on current and historical health states Premium is estimated as EPV of benets Also calculate s.e. for premium estimates Allow for best-estimate reserves and VaR Allow for calculating demographic characteristics

12/29 Solvency II SCR t = arg min x = arg min x { } Pr (NAV t+1 > 0 NAV t = x) 99.5% ) { Pr ( NAV t NAV t+1 e δ t+1 > x } 0.5% NAV t : net asset value at time t δ t+1 : interest rate from t to t + 1 Horizon: one year Interpretation: capital required to cover extreme losses

13/29 Solvency II Standard Formula For each risk (European Insurance and Occupational Pension Authority, 2011) SCR Shock t = NAV t NAV Shock t NAV t : net asset value at time t NAV t Shock : net asset value with the one-o permanent shock We consider two uncorrelated risks: longevity and disability Longevity risk: a permanent 20% decrease in mortality rates at all ages Disability risk: an increase of 35% in disability rates at all ages for the next year a permanent increase of 25% at all ages for the following years a permanent decrease of 20% in recovery rates at all ages Aggregate ( ) 2 ( SRCt S = SRC Longevity + t SRC Disability t ) 2

14/29 Solvency II Standard Formula (Cont'd) Risk margin: fair value amount required to take over the liabilities (Meyricke and Sherris, 2014) RM t = m c k=0 SCRS t+k (1 + r f ) k m: time to exhaustion c: cost of capital r f : risk-free interest rate Solvency capital requirement ratio η k (t) = SCR S t V ( t, T χ(0) = k )

15/29 Topic coverage 1 Introduction 2 Methodology Health Dynamics Base Products: Thiele's Dierent Equation Products with Typical Feature: Simulation-Based Approach Solvency Capital Requirements 3 Results Demographic Characteristics Premiums Reserves Solvency Capital Requirements 4 Conclusions

No. of Disabled 10 3 6 5 Mildly disabled males Severely disabled males Mildly disabled females Severely disabled females Number of disabled 4 3 2 1 0 65 70 75 80 85 90 95 100 Figure. Number of disabled in the simulated cohorts: 65-year-old healthy individuals of 40,000 males and 40,000 females. Age

16/29 LTC Risks Table. Demographic characteristics of the simulated cohorts, based on HRS data. Demographic Characteristics Males Females Mean years of life after age 65 16.3 19.4 Mean years with mild disability 1.8 2.8 Mean years with severe disability 0.9 1.7 Share with disability 56% 73% Share with mild disability 48% 63% Share with severe disability 27% 42% Average age of rst disability, conditional on becoming disabled 76.2 76.5 Average age of rst mild disability, conditional on becoming 75.8 76.4 mildly disabled Average age of rst severe disability, conditional on becoming severely disabled 80.5 81.7 Note: The simulated cohorts are 65-year-old healthy individuals, including 40,000 males and 40,000 females.

Stand-Alone LTCI Premiums - Age and Health Age Table. Premiums for base stand-alone LTC insurance. Males Females Lump sum Continuous Annual Monthly Lump sum Continuous Annual Monthly Sold to the healthy 55 15,923 1,138 1,126 95 27,526 1,825 1,806 152 65 17,448 1,619 1,596 135 30,313 2,535 2,501 211 70 17,915 1,964 1,933 163 31,469 3,084 3,036 257 Sold to the mildly disabled 55 28,694 2,326 2,295 194 48,865 3,647 3,607 304 65 32,622 3,639 3,581 303 47,391 4,550 4,482 379 70 32,590 4,417 4,340 368 47,163 5,412 5,318 450 Sold to the severely disabled 55 130,655 - - - 157,337 - - - 65 136,771 - - - 159,412 - - - 70 131,552 - - - 154,487 - - - 17/29 The LTC insurance pays $100 per day while the insured is severely disabled - $36k p.a. assumed average care costs in residential care Interest rate 4% continuous compounding

18/29 Rider Benet and LCA Premiums Table. Premiums of base rider benet policies and life care annuities (LCA) Age Males Females Rider benet LCA H LCA M LCA S Rider benet LCA H LCA M LCA S 55 226,927 267,773 250,787 270,261 209,708 298,983 290,061 323,363 60 258,649 240,319 222,786 239,606 239,785 273,634 263,741 292,932 65 291,614 211,479 194,002 208,682 272,847 245,530 234,859 259,514 70 324,797 182,067 165,388 178,927 307,940 215,110 204,025 224,654 75 357,067 153,053 137,878 151,417 343,570 183,191 172,404 190,228 80 387,212 125,472 112,263 126,759 377,597 150,957 141,551 157,930 The rider benet policy pays $100 per day while the insured is severely disabled and pays a death benet of $500,000 when the insured dies The life care annuity pays $50 per day while the insured is alive and additional $50 per day while the insured is severely disabled ($18k p.a. assumed residential accommodation charges)

19/29 LCA Premiums - Components Table. Lump sum premiums for life care annuities sold to the healthy and annuity factors by age and gender. Life care annuities Stand-alone policies Annuity Value Annuity Factor Age Males Females Males Females Males Females Males Females 55 267,773 298,983 15,923 27,526 259,812 285,220 14.43 15.85 60 240,319 273,634 16,766 28,913 231,936 259,177 12.89 14.40 65 211,479 245,530 17,448 30,313 202,756 230,374 11.26 12.80 70 182,067 215,110 17,915 31,469 173,110 199,376 9.62 11.08 75 153,053 183,191 18,193 32,099 143,957 167,142 8.00 9.29 80 125,472 150,957 18,403 31,924 116,271 134,995 6.46 7.50 The life care annuity pays $50 per day while the insured is alive and additional $50 per day while the insured is severely disabled ($18k p.a. assumed residential accommodation charges)

Base LTCI Premiums - Ination Protection Table. Premiums for base LTC insurance sold to 65-year-old. Males Females Without Ination With Ination Increase Without Ination With Ination Increase 1. Stand-alone policies sold to the healthy 17,448 27,930 60% 30,313 50,946 68% 2. Stand-alone policies sold to the mildly disabled 32,622 44,992 38% 47,391 69,990 48% 3. Stand-alone policies sold to the severely disabled 136,771 157,321 15% 159,412 191,237 20% 4. Rider benet policies sold to the healthy 291,614 302,097 4% 272,847 293,480 8% 5. Life care annuities sold to the healthy 211,479 280,065 32% 245,530 337,567 37% 6. Life care annuities sold to the mildly disabled 194,002 252,675 30% 234,859 318,576 36% 7. Life care annuities sold to the severely disabled 208,682 255,889 23% 259,514 332,848 28% 20/29 Interest rate 4% continuous compounding Ination rate 3% continuous compounding

21/29 LTCI Premiums - Typical Product Features Table. Impact of elimination period and maximum benet period. Elimination Males Females Period Lump sum Annual Monthly Lump sum Annual Monthly 0-day 30-day 60-day 90-day 0-day 30-day 60-day 90-day Unlimited benet period 17,018 1,510 131 29,843 2,392 207 (219) (31) (5) (287) (35) (6) 16,561 1,470 128 29,155 2,337 202 (216) (30) (5) (284) (35) (6) 16,116 1,430 124 28,479 2,283 198 (213) (30) (5) (281) (34) (6) 15,680 1,391 121 27,817 2,230 193 (210) (29) (5) (278) (34) (6) 3-year maximum benet period 10,700 950 83 17,237 1,382 120 (111) (16) (3) (128) (17) (3) 10,418 924 80 16,854 1,351 117 (109) (16) (3) (127) (17) (3) 10,142 900 78 16,476 1,321 114 (108) (16) (3) (126) (17) (3) 9,873 876 76 16,106 1,291 112 (107) (16) (3) (125) (16) (3)

22/29 Shared LTCI for Couples Allowing each spouse to access his/her partner's benets Example: 3-year shared LTCI, each spouse has potential to claim 6 years' benets For a couple of a male and a female both aged 65: Product 3-year, separate 3-year, shared 6-year, separate Premium 27,937 37,450 39,507 s.e. (239) (240) (375) Product 2-year, separate 2-year, shared 4-year, separate Premium 21,171 30,569 32,982 s.e. (173) (182) (294)

Best-Estimate Reserves - Base Stand-Alone LTCI 10 4 Sold to Healthy Sold to Mildly Disabled 10 4 3 Males Females 4 Reserve 2 1 Reserve 2 0 0 70 80 90 100 70 80 90 100 Age Age Sold to Severely Disabled 10 5 1.5 Reserve 1 0.5 3/29 0 70 80 90 100 Age

24/29 VaR - Base Stand-Alone LTCI, Males 5 105 4 3 Best-estimate VaR 95% VaR 99% VaR 99.5% 2 1 0 65 70 75 80 85 90 95 100 Age

25/29 Idiosyncratic Risk - Stand-Alone LTCI, Males VaR 99.5% Best-Estimate Reserve Best-Estimate Reserve 100 Base 30-day 60-day 90-day 100 Base 5-year 4-year 3-year 50 Ratio 50 0 70 80 90 100 0 70 80 90 100 Age Age Stand-alone LTCI sold to 65-year-old healthy individuals.

26/29 Solvency Capital Requirements - Eect of Health η k (t) = SCRt S V ( ), k {H, M, S} t, T χ(0) = k 0.4 Healthy Mildly disabled Severely disabled 0.4 Healthy Mildly disabled Severely disabled Ratio 0.2 0.2 0 70 80 90 100 0 70 80 90 100 Age Age Base stand-alone LTCI sold to 65-year-old individuals.

27/29 Solvency Capital Requirements - Dierent Products η H (t) = SCR S t V ( t, T χ(0) = H ) 0.6 Stand-alone Life insurance with LTC rider Life care annuity 0.6 Stand-alone Life insurance with LTC rider Life care annuity Ratio 0.4 0.2 0.4 0.2 0 70 80 90 100 0 70 80 90 100 Age Age Base products sold to 65-year-old healthy individuals.

Solvency Capital Requirements - Management Actions Management can take actions in the presence of adverse situations Delay in management actions Base annual premium LTCI policies sold to 65-year-old healthy males Solvency capital requirements per dollar provision 0.3 Delay: 1 year Delay: 2 years Delay: 5 years 0.2 Delay: 10 years No management actions 0.1 28/29 0 65 70 75 80 85 90 95 100 Age

29/29 Topic coverage 1 Introduction 2 Methodology Health Dynamics Base Products: Thiele's Dierent Equation Products with Typical Feature: Simulation-Based Approach Solvency Capital Requirements 3 Results Demographic Characteristics Premiums Reserves Solvency Capital Requirements 4 Conclusions

29/29 Conclusions Premium and reserve: Thiele's dierential equation and simulation-based approach Solvency Capital Requirements: Solvency II standard formula LTCI product design: use of xed benets, elimination period, maximum benet period, combining with life insurance or annuities, ination protection, shared LTCI. Potential market to underwrite disabled individuals, in terms of premium and capital Maximum benet period is eective in making LTCI more aordable and reducing idiosyncratic risk Quick management actions can eectively reduce SCRs.

References Colombo, F., Llena-Nozal, A., Mercier, J., and Tjadens, F. (2011). Help wanted? Providing and paying for long-term care. OECD Health Policy Studies. OECD Publishing, Paris, France. Congressional Budget Oce (2004). Financing long-term care for the elderly. Availabe at http://www.cbo.gov/publication/15584. European Insurance and Occupational Pension Authority (2011). The fth quantitative impact study for Solvency II. Availabe at https://eiopa.europa.eu/en/consultations/qis/ insurance/quantitative-impact-study-5/index.html. Fong, J. F., Shao, A. W., and Sherris, M. (2013). Multi-state actuarial models of functional disability. UNSW Australian School of Business Research Paper No. 2013ACTL14. Glendinning, C., Davies, B., Pickard, L., and Comas-Herrera, A. (2004). Funding long-term care for older people: Lessons from other countries. Joseph Rowntree Foundation, York, U.K. Meyricke, R. and Sherris, M. (2014). Longevity risk, cost of capital and hedging for life insurers under Solvency II. Insurance: Mathematics and Economics, 55(forthcoming), 147155. Productivity Commission of Australia (2011). Caring for older Australians. Final Inquiry Report No. 53. Available at http://www.pc.gov.au/projects/inquiry/aged-care/report. Productivity Commission of Australia (2013). An ageing Australia: Preparing for the future. Commission Research Paper. Available at http://www.pc.gov.au/ data/assets/pdf_file/0005/129749/ageing-australia.pdf. Shi, P. and Zhang, W. (2013). Managed care and health care utilization: Specication of bivariate models using copulas. North American Actuarial Journal, 17(4), 306324.

Appendix - Varying LTC Disability Denitions Table. Premiums for base LTC insurance sold to 65-year-old. Males Females 3+ ADLs 2+ ADLs Dierence 3+ ADLs 2+ ADLs Dierence 1. Stand-alone policies sold to the healthy 17,448 28,059 61% 30,313 47,473 57% 2. Stand-alone policies sold to the mildly disabled 32,622 48,756 49% 47,391 68,184 44% 3. Stand-alone policies sold to the severely disabled 136,771 148,445 9% 159,412 175,380 10% 4. Rider benet policies sold to the healthy 291,614 302,290 4% 272,847 290,170 6% 5. Life care annuities sold to the healthy 211,479 216,727 2% 245,530 253,939 3% 6. Life care annuities sold to the mildly disabled 194,002 205,040 6% 234,859 247,994 6% 7. Life care annuities sold to the severely disabled 208,682 227,793 9% 259,514 279,606 8% 3+ ADLs: Inured receive LTC benets when having diculties with 3 or more ADLs 2+ ADLs: Inured receive LTC benets when having diculties with 2 or more ADLs