1 Lessons in Disability ModelingProf. Philippe Maeder, Fasecolda, Bogota, 9 May 2017
2 Table of Contents / AgendaProduct Design Disability Models Actuarial Monitoring Conclusion and Discussion
3 Product Design
4 When is a Person Disabled?If the insured is unable to get an income (economic definition) and / or in case of physical impairments (physiological definition) the economic definition can rely upon own, own or similar or any occupation; the physiological one can depend on Activities of Daily Life or Activities of Daily Working. Economic definition “Own Occ.”: totally unable through sickness or accident to follow own occupation and not following any other for profit or reward “Own or similar Occ.”: totally unable through sickness or accident to follow any occupation for which the insured is reasonably suited by education, training or experience and not following any other for profit or reward “Any Occ.”: totally unable by reason of sickness or accident to follow any occupation for profit or reward Partial and / or temporary disability, or cover against Total and Permanent Disability (TPD)
5 Activities of Daily Working (ABI Definition)An insured, who is unable to do 3 specified work tasks ever again, is considered as disabled: Walking: the ability to walk more than 200 meters on a level surface Climbing: the ability to climb up a flight of 12 stairs and down again, using the handrail if needed Lifting: the ability to pick up an object weighing 2kg at table height and hold for 60 seconds before replacing the object on the table Bending: the ability to bend or kneel to touch the floor and straighten up again Getting in the ability to get into a standard saloon car, and out again & out of a car Writing: the manual dexterity to write legibly using a pen or pencil, or type using a desktop personal computer https://www.abi.org.uk/globalassets/sitecore/files/documents/publications/public/2014/pro tection/statement-of-best-practice-for-critical-illness-cover-dec-2014.pdf
6 Cover Definition Choice of Disability Definition:Mixed solutions are possible, e.g. “Own occupation”: first 1 to 2 years “Own or similar occupation” afterwards; Accidental risks can be excluded (if they are covered by other social insurances); Some definitions (physical impairment) exclude mental diseases and back pain. Define a waiting (or elimination) period: in weeks (4, 13, 26, 52) or months (3, 6, 12, 24); Define Disability Degree (for partial disability covers). Example:
7 Product Definition – Dangerous FeaturesCOLA: Cost of Living Adjustments must be limited with a ceiling. Term Age: avoid definitions referring to “normal retirement age” or any such plan definition: it can change in time and annuities get due for longer than expected and priced for. Premium Rate Guarantee: statistical history shows that incidence rates can vary upwards or downwards; offering a premium guarantee implies the inclusion of an assumed deterioration rate. Social Security definition: an easy definition is to stipulate an insured is disabled if he is recognised as disabled by Social Security. Actually such official definitions vary in time with legal changes (at times following elections), which can lead to premium deficiencies. Insured amount: in the financial underwriting, benefits must be limited so that Replacement Ratio (after taxes) is less than 100%.
8 Disability Models
9 Model Families Start from a full set of probabilities / densities:Simple or Extended Markov Chains Continuous time models Approach with two separate sub-models: Inception / annuity models Estimate premium rates directly Manchester Unity model (pay-as-you go): short term disability only
10 Markov Chains
11 Triple State Markov Chain with RecoveryActive Disabled Dead
12 Formalised Markov Chain for DisabilityState Vector: Transition Matrix Total per line = 1
13 Observed Disability Termination Rates - MalesSource: SIA Stat. Switzerland, Group Ins , WP 3 months
14 Disability Model with Recovery depending on Age and DurationActive Disabled 1st year Disabled 2nd year Disabled 3rd year Disabled (S+1)th year Dead
15 Extended Markov Chain with Several Disability States3-State Markov Chains are simple models, but those ones are not realistic: Markov processes have “no memory”; Termination rates depend more on disability duration than age. Extending the model to several disability states addresses this critic: Markov chains with transient disability states are more realistic; However the required amount of transition probabilities to estimate increases accordingly, and these best estimates are more subject to random fluctuations. Other difficulties arise when introducing waiting periods shorter than one year; with consideration of disability degree.
16 Inception Annuity Models
17 Notation and Definitionsw waiting period (in weeks or months) prob. {disability for a duration w at least} x' age at the beginning of disability s age at which cover terminates (s = x + n) t elapsed disability duration average disability degree (at x’ + w) sx',t prob. of recovering or dying after t disabled x x+1 w x' + w x'=x+ 1 / 2
18 Model CharacteristicsDeterministic survivorship group of disabled: Present value of a disability annuity: In practice, assume x = x’, which ensures a conservative rounded age. Annual risk premium: with a constant disability degree g and a loading for claims management b.
19 Annual and Risk Premium
20 Active Life Reserves – Level Premium Tariffs
21 Pricing and Reserving Aspects to ConsiderLevel Premium Financing also leads to negative Active Life Reserves (ALR). Are negative reserves acceptable on a statutory basis? Usually not. One needs to check whether the regulator accepts a compensation with (positive) provisions on life benefits for policies combining both covers. For waiting periods of one or two years, there is no more chances to get benefits in case of disability in the last one or two years of the policy while a premium is still due. This feature can be avoided by limiting the premium payment duration to at most n – w. Else there is a risk of cancellation of the policy (for stand-alone covers essentially) while the ALR is negative. For Group Life contracts, only annual risk premium financing can be considered.
22 Risk Segmentation and Trends
23 Risk Segmentation and TrendsThe most common segmentation criterion is the occupation (individual insurance) or the economic activity (group insurance); They influence not only incidence rates, but also termination rates; Differentiation by smoker status is less significant than in the area of mortality. Trends: A Relation between unemployment rate and disability incidence rate has been demonstrated, at least for shorter waiting periods; In the long term, the trends are unpredictable; Usually, a deterioration of incidence rates (increasing with time) is accompanied by a deterioration of termination rates (decreasing with time).
24 Occupational Classes Professional White Collars: Professional, managerial, executive, administrative and clerical classes not engaged in manual labour; Tradesmen, Foremen: Master craftsmen & tradesmen engaged in management & supervision; Skilled operatives engaged in light manual work in non-hazardous occupations; Skilled Craftsmen: Skilled and semi-skilled operatives engaged in heavy manual work or subject to special hazard; Heavy Labourers, Miners: Skilled and semi-skilled operatives engaged in heavy manual work or subject to special hazard.
25 Disability Incidence Rates per Class UK - Males - % 1975/78 StandardSource: Continuous Mortality Investigation Bureau C.M.I.R. Reports 2, 4, 7, 11, 15, 18
26 Recovery According to Occupation UK - Males - DP 13 weeksSource: Continuous Mortality Investigation Bureau C.M.I.R. Reports 2, 4, 7, 11, 15, 18
27 Disabled Mortality by Occupation UK - Males - DP 13 weeksSource: Continuous Mortality Investigation Bureau C.M.I.R. Reports 2, 4, 7, 11, 15, 18
28 Incidence Rates - Group Insurance Males, Switzerland, WP= 3 monthsSource: Swiss Insurance Association
29 Termination Rates - Group Insurance Males, SwitzerlandSource: Swiss Insurance Association
30 Disability and Unemployment - Switzerland
31 Actuarial Monitoring
32 Technical Accounts for Disability - Example
33 Disability Products: What shall we Monitor?Various quantities must be periodically measured in order to adjust pricing and reserving bases within an incidence / annuity model: disability incidence rates, active lives mortality, disabled persons recovery and mortality rates (or together as termination rates), disability degree. Those statistics are more complex than mortality measures: claims data take a long time to develop (notification / allocation time imply a high level of IBNR); With long waiting periods, the age at start of payment may be higher than the age at disability inception; Multiple decrements intervene in disabled lives statistics; Material may be (hopefully) scarce for claims in course of payment.
34 Conclusion and Discussion
35 Lessons from Disability ModelingThe best pricing model will be inefficient if product definition and underwriting were not made according to the best standards. The choice of a pricing model consists of reaching a compromise between model complexity and availability of data to calibrate it. The incidence / annuity model looks like the best approach for disability income products. there is no need to monitor recovery and mortality of disabled separately; disability incidence rates and termination rates can be updated independently depending on the experience measured on one or the other side; Segmentation of risks must be performed to avoid attracting bad risks from the market.
36 Questions – the Floor is yours!
37
38 Legal notice ©2017 Swiss Re. All rights reserved. You are not permitted to create any modifications or derivative works of this presentation or to use it for commercial or other public purposes without the prior written permission of Swiss Re. The information and opinions contained in the presentation are provided as at the date of the presentation and are subject to change without notice. Although the information used was taken from reliable sources, Swiss Re does not accept any responsibility for the accuracy or comprehensiveness of the details given. All liability for the accuracy and completeness thereof or for any damage or loss resulting from the use of the information contained in this presentation is expressly excluded. Under no circumstances shall Swiss Re or its Group companies be liable for any financial or consequential loss relating to this presentation.