Practical Example of a Split Accelerated Critical Illness Insurance Product Anton Brink, Ph.D. RGA UK Services Limited
Presentation Disclaimers: Contains all personal views based on external research These views are not representative of RGA or its clients Methodology utilises illustrative examples Not meant to be used as a prescriptive guide on how to price Buy-Back CI 2
Overview of Presentation CI Limitations & Available Buy-Back Products PMI Data to determine Option Premium for a Multi-State Buy-Back Model Determine Buy-Back Option Premium for a Restricted set of CI Conditions Results for Buy-Back Option Premiums Conclusions & Further Work 3
Critical Illness Conditions Cancer Cardiovascular Neurological Other 4
Main Limitation of CI Only a single claim is payable with CI product Reinstatement of CI benefit is then very expensive as claimant perceived to be at a higher risk of further CI claim incidences or earlier death Avoided if a buy-back option had been purchased at the initial policy inception for a small additional premium 5
Buy-Back Available in Australia 100% of the amount of any claim will be reinstated with no further medical evidence one year from the date your claim was accepted. The same condition or connected (e.g. stroke after heart attack) is excluded Particular conditions are excluded, e.g. T.I., T.P.D. Need to select option initially at additional premium Zurich - Stepped annual reinstatement to full benefit Maximum purchase age 60, buy-back ceases at age 70 6
or Cover Reinstatement in the U.K. But only certain conditions can be reinstated E.g. Scottish Provident: Heart attack, Stroke and Cancer Limit of reinstatement % of S.A. or 100,000 The cost of the buy-back is around 10% of premium Other considerations: Guaranteed/Reviewable Premium Rates Full, reduction or Waiver of subsequent Premiums We have not included any restrictions in our analysis 7
Overview of Presentation CI Limitations & Available Buy-Back Products PMI Data to determine Option Premium for a Multi-State Buy-Back Model Determine Buy-Back Option Premium for a Restricted set of CI Conditions Results for Buy-Back Option Premiums Conclusions & Further Work 8
Data Problems Once a policyholder makes a valid 1 st claim, the CI coverage ceases So no insured CI data available to determine a 2 nd CI incidence rate Utilise instead Private Medical Insurance (PMI) or Medical Expenses settled claimant data, where repeat claims are recorded 9
PMI Data for Buy-Back Model Our Female Data of 1 st, 2 nd PMI Claims 10
Problems with PMI Data Amounts too small & frequent compared to large & infrequent CI claims Claims are not pre-assigned into different incidents Need to assume a time-break (of say 180 days) between claims to signify separate incidents Different type of claim definition, policyholder profile, underwriting approach etc. With these problems in mind, build a model 11
Standard Life Model D: Death M H: Healthy W: Withdrawal Transition from State H to D Payable M 12
Accelerated Critical Illness (ACI) HD: Death with no incidents M H: Healthy M A: Post 1 st Qualifying HW: Withdrawal with no incidents Transition from State H to D H to A Payable M M 13
Partial ACI Model HD: Death with no incidents M H: Healthy AD: Death Post 1 st Qualifying M b M (1-b ) A: Post 1 st Qualifying AW: Withdrawal Post 1 st Qualifying HW: Withdrawal with no incidents b Model 100% Standard ACI % Life Reinstatement 0% Standard Life Transition from State H to D H to A Payable M M x b A to D M x (1- b) 14
General Buy-Back Model HD: Death with no incidents M H: Healthy AD: Death Post 1 st Qualifying Mxb M (1-b ) A: Post 1 st Qualifying AW: Withdrawal Post 1 st Qualifying Mx(1-b) BD: Death Post 2 nd Qualifying B: Post 2 nd Qualifying HW: Withdrawal with no incidents BW: Withdrawal Post 2 nd Non- Qualifying b All Condition CI Model 100% Standard ACI % Full 100% buy-back 0% Our Delayed Transition from State H to D H to A Payable M M x b A to B, A to D M x (1- b) 15
Methodology Probabilities For each of the main condition groups Paid claim counts developed to obtain expected diagnosed claims Found fitted 1 st incidence rates by graduating the developed claim counts from state H to state A exposure in state H Similarly, 2 nd incidence rates from state A to state B, death & withdrawal incidence rates Corresponding probabilities found using formula for Kolmogorov forward differential equations 16
Methodology Profit Margin (PM) For a particular choice of main condition group Probabilities used to build a profit cash flow model Expected Profit = expected premiums - expected benefits - change in expected reserves for each year of policy term Chose summary statistic to compare models Profit margin (PM) = Total discounted expected profit Total discounted expected premium Found premium corresponding to a 20% profit margin (before expenses, commissions, tax etc.) Rescaled premium in order that a 40 year old female with a standard ACI only product would pay 100 17
20 30 40 60 0% (Impaired) 100% (ACI) 25% 20 75% % (Buy-Back) 30 40 60 Relative Premium Relative Premium General Buy-Back Model Relative Premium for 20% Profit Margin for Selected Buy-Back % s with Increasing Age 275 2 225 200 175 1 125 100 75 Relative Premium Required for a 20% Profit Margin for Increasing Age 0% (Impaired) 25% % (Buy-Back) 75% 100% (ACI) Relative Premium Required for a 20% Profit Margin 275 2 225 200 175 1 125 100 75 25 0 Age 25 0 % b Age 18
0% (Impaired) 100% (ACI) 25% 20 75% % (Buy-Back) 30 40 60 Relative Premium Relative Premium General Buy-Back Model Relative Premium for 20% Profit Margin for Selected Ages with Increasing Buy-Back % s 275 Relative Premium Required for a 20% Profit Margin for Increasing % of Premium Payable on 1st Relative Premium Required for a 20% Profit Margin 2 2 225 200 175 1 20 30 40 60 225 200 175 1 125 100 75 125 100 25 0 75 Age 25 0 0% (Impaired) 25% % (Buy-Back) 75% 100% (ACI) Age % b 19
% (Buy-Back) 25% 0% (Impaired) 100% (ACI) 20 75% 30 40 60 Relative Premium General Buy-Back Model Relative Premium Required for a 20% Profit Margin 275 2 225 200 175 1 125 100 75 25 0 Age % b 20
% (Buy-Back) 25% 0% (Impaired) 100% (ACI) 20 75% 30 40 60 Relative Premium General Buy-Back Model 2-275 225-2 200-225 175-200 1-175 125-1 100-125 75-100 -75 25-0-25 Relative Premium Required for a 20% Profit Margin 275 2 225 200 175 1 125 100 75 25 0 Age % b 21
% (Buy-Back) 25% 0% (Impaired) 100% (ACI) 20 75% 30 40 60 Relative Premium General Buy-Back Model 2-275 225-2 200-225 175-200 1-175 125-1 100-125 75-100 -75 25-0-25 Relative Premium Required for a 20% Profit Margin 275 2 225 200 175 1 125 100 75 25 0 Age % b 22
% (Buy-Back) 25% 0% (Impaired) 100% (ACI) 20 75% 30 40 60 Relative Premium General Buy-Back Model 2-275 225-2 200-225 175-200 1-175 125-1 100-125 75-100 -75 25-0-25 Relative Premium Required for a 20% Profit Margin 100% 40 275 2 225 200 175 1 125 100 75 25 0 Age % b 23
% (Buy-Back) 25% 0% (Impaired) 100% (ACI) 20 75% 30 40 60 Relative Premium General Buy-Back Model 20% PM 2-275 225-2 200-225 175-200 1-175 125-1 100-125 75-100 -75 25-0-25 Relative Premium Required for a 20% Profit Margin 100% 57 47 40 275 2 225 200 175 1 125 100 75 25 0 Age % b 24
% (Buy-Back) 25% 0% (Impaired) 100% (ACI) 20 75% 30 40 60 Relative Premium General Buy-Back Model 20% PM 2-275 225-2 200-225 175-200 1-175 125-1 100-125 75-100 -75 25-0-25 Relative Premium Required for a 20% Profit Margin 100% 100 100 47 40 275 2 225 200 175 1 125 100 75 25 0 Age % b 25
Relative Premium Required for 20% Profit Margin Buy-Back Option Premium 1 400 3 300 2 Relative Premium Required for 20% Profit Margin Stand-Alone All Conditions Accelerated All Conditions Buy-Back All Conditions Buy - back option premium 1 Death 200 1 100-20 30 40 60 Age Notes: Premium option equal to buy-back premium less standard premium Relative to a 40 year old female with a standard ACI product costing 100 26
Overview of Presentation CI Limitations & Available Buy-Back Products PMI Data to determine Option Premium for a Multi-State Buy-Back Model Determine Buy-Back Option Premium for a Restricted set of CI Conditions Results for Buy-Back Option Premiums Conclusions & Further Work 27
New Restricted Model CI cover expensive for an unhealthy life By unhealthy mean previous medical history of a minor non-ci complaint, e.g. slight angina Considered at a higher risk of claiming for a related CI condition, e.g. any cardiovascular Offer a restricted product which provides coverage for the remaining unrelated CI conditions 28
Basic Restricted Model Basic Solution: Only model the restricted CI conditions Ignore the other conditions related to the poor health Split our post 1st incident state into two parts a qualifying state A for those conditions with a benefit payment a non-qualifying state A other for the remaining nonbenefit conditions 29
Basic Restricted Model HD: Death with no incidents M H: Healthy AD: Death Post 1 st Qualifying M b Mx(1-b ) A: Post 1 st Qualifying AW: Withdrawal Post 1 st Qualifying Model Basic Restricted b 100% HW: Withdrawal with no incidents M A Other D: Death Post 1 st Non- Qualifying A Other : Post 1 st Non-Qualifying A Other W: Withdrawal Post 1 st Non- Qualifying Transition from State H to D, A other to D H to A Payable M M x b A to D M x (1- b) 30
Problem with Basic Model However, basic model ignores non-qualifying conditions Unhealthy life may contract one of the nonqualifying conditions as an intermediate step, before satisfying one of the qualifying conditions If the incidence from a non-qualifying condition to a qualifying condition is higher than from the healthy state, then the basic model underestimates the required premium 31
Standard Restricted Model Include non-qualifying conditions To include the above we need to allow a further transition from the non-qualifying state A other to say a qualifying state B Where State B has the same conditions as the qualifying state A 32
Standard Restricted Model HD: Death with no incidents M H: Healthy HW: Withdrawal with no incidents AD: Death Post 1 st Qualifying M b M (1-b ) M A Other D: Death Post 1 st Non- Qualifying A: Post 1 st Qualifying A Other : Post 1 st Non-Qualifying AW: Withdrawal Post 1 st Qualifying M A Other W: Withdrawal Post 1 st Non- Qualifying BD: Death Post 2 nd Qualifying B: Post 2 nd Qualifying BW: Withdrawal Post 2 nd Non- Qualifying Transition from State H to D, A other to D, A other to B H to A Model Standard Restricted b 100% Payable M M x b A to D M x (1- b) 33
Example for Individual Conditions It may appear appealing to find premiums for our grouped main condition models: cancer only model, cardiovascular only model, neurological only model. However, we cannot add the premiums together from a menu of such grouped condition models in order to determine the premium for a model with a tailored set of grouped conditions In particular, the premiums do not sum to the premium for an All Conditions model 34
Premium for Standard Restricted Models Relative Premium for a 20% Profit Margin in each Individual Condition for the "Simplified" ACI Model 60 Age 40 30 All Neurological All Cardiovascular All Malignant Cancer All CI 20 0% % 100% 1% 200% 2% 300% Relative Premium for a 20% Profit Signature 35
General Restricted Buy-Back Model HD: Death with no incidents M H: Healthy HW: Withdrawal with no incidents AD: Death Post 1 st Qualifying Mxb M (1-b ) M A Other D: Death Post 1 st Non- Qualifying A: Post 1 st Qualifying A Other : Post 1 st Non-Qualifying AW: Withdrawal Post 1 st Qualifying Mx(1-b) M A Other W: Withdrawal Post 1 st Non- Qualifying BD: Death Post 2 nd Qualifying B: Post 2 nd Qualifying BW: Withdrawal Post 2 nd Non- Qualifying Transition from State H to D, A other to D, A other to B H to A Model Buy Back Restricted b % Payable M M x b A to B, A to D M x (1- b) 36
Relative Accelerated Cancer Premium Premium for Cancer Conditions 400 3 300 2 200 Relative Accelerated Cancer Only Premium for a 20% Profit Margin Buy-Back Restricted Cancer Standard Cancer Basic Cancer buy-back option Premium 2 intermediary nonqualifying conditions 1 100 0 20 30 40 60 Age Notes: Premiums for full benefit payment M on 1 st incident Relative to a 40 year old female with a standard cancer only product costing 100 37
General Restricted Buy-Back Model Can also exclude certain parts of a CI condition e.g. as an extreme case, breast cancer from our previous female cancer only product 38
Relative Accelerated Cancer Premium Premium for Cancer (ex breast) 400 3 300 Relative Accelerated Cancer Only Premium for a 20% Profit Margin Buy-Back Restricted Cancer Buy-Back Restricted Cancer (ex breast) Standard Cancer Decrease in premium on excluding breast cancer 2 200 Basic Cancer 1 100 0 20 30 40 60 Age 39
Relative Accelerated Cancer Premium Premium for Cancer (ex breast) 400 3 300 2 Relative Accelerated Cancer Only Premium for a 20% Profit Margin Buy-Back Restricted Cancer Buy-Back Restricted Cancer (ex breast) Standard Cancer Standard Cancer (ex breast) Basic Cancer buy-back option Premium 3 200 1 100 0 20 30 40 60 Age 40
Relative Accelerated Cancer Premium Premium for Cancer (ex breast) 400 3 Relative Accelerated Cancer Only Premium for a 20% Profit Margin Buy-Back Restricted Cancer (ex breast) 300 2 200 1 Standard Cancer (ex breast) Basic Cancer (ex breast) buy-back option Premium 3 intermediary nonqualifying conditions 100 0 20 30 40 60 Age 41
Overview of Presentation CI Limitations & Available Buy-Back Products PMI Data to determine Option Premium for a Multi-State Buy-Back Model Determine Buy-Back Option Premium for a Restricted set of CI Conditions Results for Buy-Back Option Premiums Conclusions & Further Work 42
Relative Option Premium Required for a 20% Profit Margin Buy-Back Option Premiums 1 to 3 140 120 Relative Buy-Back Option Premium Required for a 20% Profit Margin Buy-Back Buy-Back Margin Option All Premium Conditions1 All Conditions Buy-Back Option Cancer Premium 2 Cancer 100 Buy-Back Buy-Back Option Option Cancer Premium (ex Breast) 3 Cancer (ex Breast) 80 60 40 20 0 20 30 40 60 Age Notes: Premium option equal to buy-back premium less Standard premium Relative to a 40 year old female with a standard Cancer only product costing 100 43
Overview of Presentation CI Limitations & Available Buy-Back Products PMI Data to determine Option Premium for a Multi-State Buy-Back Model Determine Buy-Back Option Premium for a Restricted set of CI Conditions Results for Buy-Back Option Premium Conclusions & Further Work 44
Conclusions Presented multi-state models To determine the buy-back premium, while Allowing any non-qualifying conditions to act as an intermediary state before a qualifying condition Found different buy-back premium curves by age when we have all the conditions, a restriction to cancer only or cancer only, but excluding breast cancer 45
Conclusions The buy-back premium option curves indicate An increase of 30% at age 20 to 55% at age 60 in the non buy-back model premium This fairly high cost of the buy-back option premium is likely to result from including small multiple claims data Introducing restrictions to the buy-back option would reduce the premium 46
Further Work Further analysis of the PMI database to better match the data to typical CI incidence rates Determining the size of reductions to the buy-back premium on applying the restrictions discussed in the introduction Further details in the corresponding paper at www.ica2010.com Any Questions? 47
Contact Details Anton Brink RGA UK Services Limited 16th Floor, 5 Aldermanbury Square, London, EC2V 7HR T +44207 710 6831 abrink@rgare.com 48