Trafficlight extended with stress test for insurance and expense risks in life insurance


 Egbert Reynolds
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1 PROMEMORIA Datum 0 July 007 FI Dnr Fnansnspetonen Författare Bengt von Bahr, Göran Ronge Traffclght extended wth stress test for nsurance and expense rss n lfe nsurance Summary Ths memorandum comprses the bass for stress testng wthn the traffclght method. The memorandum ncludes the stress of those parts of the techncal provsons that comprse nsurance rss,.e. mortalty, morbdty and lapse rss. Expense rs s also consdered. P.O. Box 6750 SE Stocholm [Sveavägen 167] Tel Fax Bacground and purpose Fnansnspetonen s now developng a stress test for nsurance companes entre operatons that covers both assets and labltes. The sze of the changes n the rs assumptons wll be chosen so that they represent approxmately the 99.5 percent quantle for the possble outcomes over the term of one year. Ths memorandum descrbes how the rs assumptons n lfe nsurance companes shall be stressed. For some assumptons, e.g. those that relate to longterm trend forecasts for mortalty and morbdty, the sze of these changes cannot be quantfed n ths manner. In these cases, the assumptons are based on CEIOPS wor for Solvency II. Lfe nsurance companes that have shortterm llness and accdent nsurance classfed as nonlfe nsurance, report t n the same manner as other nonlfe nsurance. Refer to parts of the specal nstructons for Traffc lght Nonlfe nsurance. Nonlfe companes wth annutes emanatng from nonlfe nsurance, report accordng to that specal secton n ths memorandum. Changed assumptons for lfe nsurance The assumptons refer to assumptons made n the valuaton of techncal provsons. The stressed provsons shall consst of Best provsons n accordance wth the Prudent Person Prncple An ncrease n the provsons on account of a reducton n the dscount rate (the default alternatve) An ncrease n the provsons on account of stressed rs assumptons 1(10)
2 Best provsons n accordance wth the Prudent Person Prncple Best provsons accordng to the Prudent Person Prncple shall correspond to the expected value of the future dscounted payments for the company s nsurance rss. The calculatons shall be made wth adequate actuaral methods wthout mplct general securty loadngs. Dscountng should be made wth a rsfree nterest rate. Reducton of the dscount rate The stressng of assumptons regardng the dscount rate s presented n the nstructons for the stress test for lfe nsurance companes. Ths topc s not dscussed n detal here. Stressng of other rss Instructons for stress tests relatng to mortalty rs, morbdty rs, nonlfe annuty rs and lapse rs, all of whch are ncluded under the term nsurance rs, are presented below. In addton, an expense rs s dentfed and reported separately. Rss relatng to shortterm llness and accdent nsurance that are classfed under nonlfe nsurance but are managed by lfe nsurance companes follow the regulatons that apply to correspondng rss wthn nonlfe nsurance companes. Assumptons regardng poltcal rss, for example fscal rs, are classfed as operatng rss and not dscussed here. Mortalty rs Volatlty rs The best estmate of mortalty outcome for the comng year may be defned as BSU = p R aggregated over all nsurances (or rather all nsured lves) n all portfolos, where p s the best estmate of the oneyear mortalty probabltes and R s the best estmate of rs sums, both postve and negatve.
3 The captal requrement for volatlty rs s measured wth the standard devaton for the outcome n the comng year, whch s Sd( BSU ) = p (1 p ) R. If ths sum s dffcult to calculate, t may be approxmated by p (1 p) p( 1 p) R, where p s an average probablty, or by R, n where n s the number of rss. In order to ncrease the precson of the estmate of p, t s possble to dvde the portfolo nto subpopulatons wth more homogeneous age compostons. The average probablty shall preferably be weghted by the rs sum and may be determned from the data presented n the Actuaral Report. The captal requrement for volatlty rs s.58 Sd(BSU). If the company has a stoploss, cumulatve or other types of long rensurance (nonnegotable on a oneyearbass), the company may modfy the above estmate of volatlty rs. The modfcaton shall be ustfed. Note It may appear llogcal n the calculaton of the volatlty rs to also nclude the outcome of the negatve rs sums. The volatlty rs should be a measurement of the sze of postve devatons from the expected value,.e. outcome that s larger than expected. Postve devatons may occur n two ways, ether an exceptonally large number of postve rs sums or an exceptonally small number of negatve rs sums occur. The volatlty rs shall therefore be calculated on the bass of the entre portfolo of rs sums. Parameter rs The techncal nsurance provsons shall be estmated usng the mortalty assumptons that comprse the best estmate accordng to the Prudent Person Prncple. These provsons are desgnated as BA. Wth respect to the choce of mortalty assumptons, the followng apples. The company shall apply assumptons regardng current and future mortalty to ts portfolo on the bass of experence from ts own and smlar nsurance populatons. For ths purpose, the company may apply sutable parts of results concernng mortalty for dfferent nsurance populatons emanatng from the report publshed by DUSommttén, the Swedsh Research Councl for Actuaral Scence under the Swedsh Insurance Federaton. For annutes emanatng from nonlfe nsurance, the common mortalty assumptons used among nsurers may be used. Some comparatve estmates from mortalty stressng are reported n Appendx 1. These show that a general factor reducton n mortalty by approxmately 0 percent corresponds to an ncreased expected lfespan for a 65yearold (both male and female) of years. Correspondngly, a factor ncrease n mortalty 3
4 means that the probablty that a 40yearold des before the age of 65 ncreases by 81%. CEIOPS uses smlar technques n Solvency II. The stressng s mplemented by calculatng the provsons wth other mortalty assumptons as follows: The oneyear mortalty probablty s ncreased by 0% n all ages The oneyear mortalty probablty s reduced by 0% n all ages Of these two stressngs, the company shall choose the one whch gves the hghest provsons. Ths s denoted by SA. max SA BA;0. The captal requrement for parameter rs s ( ) The captal requrement for mortalty rs s calculated wth a rootsquare formula from volatlty rs and parameter rs. Morbdty rs Morbdty rs refers to the nsurance rs wthn longterm llness nsurance and waver of premum nsurance. Volatlty rs The best estmate of the morbdty outcome for the comng year may be defned as BSU = p P q Q r R, where the frst sum ncludes all nsurances except ongong cases of llness, the second all ongong cases of llness pror to the end of the qualfyng perod and the thrd all cases of llness n payment. p s the best estmate of the oneyear probablty of llness ncdence and P s the correspondng estmate of the rs sum. q s the best estmate of the probablty that the llness wll termnate wthn one year for those cases of llness that are n the qualfyng perod and Q s the correspondng estmate of the released rs sum. r s the best estmate of the probablty that cases of llness n payment wll termnate wthn one year and R s the correspondng estmate of the released rs sum. 4
5 Note: In some companes, the llness s frst regstered when payments wll begn. In such cases, the above qq terms may be approxmated or placed n pp terms. Insurances that nclude benefts wth varyng qualfyng perods should be dvded nto correspondng portfolo components. The volatlty rs s measured wth the standard devaton for the outcome n the comng year, whch s Sd( BSU) = p (1 p ) P + q (1 q ) Q + r (1 r ) R. If these sums are dffcult to calculate, they may be approxmated n a smlar manner as descrbed n Mortalty rs. The captal requrement for volatlty rs s.58 Sd(BSU). If the company has a stoploss, cumulatve or or other types of long rensurance (nonnegotable on a oneyearbass), the company may modfy the above estmate of volatlty rs. The modfcaton shall be ustfed. Parameter rs The techncal nsurance provsons shall be estmated usng the assumptons that comprse the best estmate accordng to the Prudent Person Prncple. The same prncples apply here as for parameter rss n Mortalty rs. These provsons are desgnated as BA. The stressng s mplemented by applyng the followng other assumptons: ncreased oneyear probabltes of llness ncdence by 50% reduced probabltes by 0% at all tmes that the llness has termnated. If the company apples a run off functon λ(x,t), ths shall be ncreased such that [1 λ(x,t)] s replaced by 0.8 [1 λ(x,t)] for all ages x and duratons t. the degrees of nvaldty (the relatonshp between actual leave of absence due to llness and fulltme leave of absence due to llness), gr, s ncreased such that (1gr) s replaced by 0.8 (1gr) These provsons are desgnated as SA. The captal requrement for parameter rs s SA BA. Appendx shows the aggregated morbdty outcomes for lfe nsurance companes durng the years n accordance wth the Actuaral Report. Ths data partly verfes the stress test levels that are currently recommended. 5
6 The captal requrement for morbdty rs s calculated wth a rootsquare formula from volatlty rs and parameter rs. Annutes emanatng from nonlfe nsurance ( nonlfe annutes ) Volatlty rs The best estmate of the nonlfe annutes outcome for the comng year may be defned as BSU = p R aggregated across all nonlfe annutes, where p represents the best estmates of the oneyear mortalty probabltes and R s the best estmate of (negatvely released) rs sums. The volatlty rs s measured wth the standard devaton for the outcome n the comng year, whch s Sd( BSU ) = p (1 p ) R. If ths sum s dffcult to calculate, t may be approxmated n a smlar manner as descrbed n Mortalty rs. The captal requrement for volatlty rs s.58 Sd(BSU). Parameter rs The techncal nsurance provsons shall be estmated usng the assumptons that comprse the best estmate accordng to the Prudent Person Prncple. The same prncples apply here as for parameter rss n Mortalty rs. These provsons are desgnated as BA. The stressng s mplemented by calculatng the provsons wth a mortalty assumpton such that the oneyear mortalty probablty s 0% lower n all ages. These provsons are desgnated as SA. The captal requrement for parameter rs s SA BA. The captal requrement for nonlfe annuty rs s calculated wth a rootsquare formula from volatlty rs and parameter rs. 6
7 Lapse rs The purpose for ntroducng lapse rs n the stress test s to see f the company has enough captal to cover losses because of 1. lapses, whch mply that polcy holders through surrenders or transfers have the rght to receve more captal than has been estmated n the calculatons of labltes and bonuses,. lapses, whch mply that the remanng captal n the company ntended to gve contrbutons to cover expences s reduced, 3. lapses, whch mply that future ncome, ntended to cover manly acquston costs already occurred, wll be severely reduced. Lapse ncludes padup polces, cessaton of premum payments, surrenders and transfers. All these types of lapses can have effect on the stress test under tem 3. above, whle only surrender and transfers have effect on tems 1. and. Pure rs nsurance and longterm morbdty nsurance are not consdered when calculatng lapse rs. Item 1 concerns probably only defned contrbuton pensons n occupatonal penson schemes and tradtonal ndvdual lfe nsurance. The company must calculate values for each polcy where the surrender value (Å) s greater than the retrospectve reserve (V ) and where the value Å s bass for full or partal rght to surrender. One should thus dsregard from polces wthout rght to surrender or transfer and those polces whch at the actual moment has V > Å. The exposure U1 under Item 1 s the sum of the dfferences between Å and V for these contracts. Item 1 s relevant even for nonmutuals where guaranteed lfe provsons plus rs absorbng bonus plays the same role as retrospectve reserve V. Otherwse an alternatve calculaton must be done wth the same purpose, dependng on polcy condtons and bonus rules. Exstng fees for surrenders and transfers may reduce the exposure U1. The bass for Item s the sum of all nsurance captals (retrospectve reserves) for all polces wth the possblty to surrender or transfer. Item concerns all savngs products, such as occupatonal pensons and ndvdual lfe nsurance. Even unt lned products and so called depost accounts must be ncluded, because lapses among these may reduce the company s ncome to cover expenses. 7
8 The exposure U under Item s obtaned by multplyng the total bass by a standard loadng 0,75 %, as ths factor s consdered an approxmaton of the expense fee, wth whch the nsurance company reduces ndvdual nsurance savngs. Item 3 concerns, as tem, only savngs products, and measures an mplct or explct clam through exstng polces on both polcy holders and agents/broers, manly regardng acquston costs and other ntal expenses. Salesmen cancellaton responsblty may be taen nto account. The tem Deferred acquston costs (DAC) from the balance sheet may be appled as a proxy for the exposure U3 under Item 3. The total exposure for lapse rs s the sum of the exposures under the three above Items. The captal requrement for lapse rs s determned as 0 % of the total exposure. Total lfe nsurance rs The total lfe captal requrement for lfe nsurance rs can now be calculated usng the followng correlaton matrx Korr Mortalty Morbdty Lapse Mortalty 1 0,5 0,5 Morbdty Lapses In the traffc lght model, the total captal requrement s consoldated from all adequate rs factors. Expense rs The purpose for testng expense rs s that the company must be able to cover an ncrease of the fxed expenses for dfferent reasons by 10 %. It s assumed that the company can reduce ths ncrease of costs and/or ncrease the ncome wthn a perod of 1 months. The stressng s thus assumed to have only a temporary effect. Ths rs shall be reported separately and shall not be ncluded under the term nsurance rs. The expense rs s measured by 8
9 K = the company s annual fxed costs, defned as operatng expenses plus clams adustment costs mnus acquston costs. The captal requrement for expense rs s calculated as 0.1 K. Expense rs and nsurance rs (mortalty, morbdty) are assumed to have a correlaton coeffcent of 50 % when calculatng the total captal requrement n the traffc lght model. *********************************************************** Appendx 1 Examples of stressed mortalty assumptons The followng table presents a comparson of the stressng between QIS and ths memorandum for P(40,65) = the probablty that a 40yearold wll de before the age of 65 E(65) = the expected remanng lfespan for a 65yearold The startng pont s the M90 mortalty table and the stress tests have been mplemented by multplyng the mortalty ntensty by a factor. Factor P(40,65) E(65) Female Male Female Male % 7.98% % 8.93% % 9.88% % 10.81% % 11.73% year years year years % % 1, % 1, % +1 year and + years ndcates the ncrease n expected lfespan n relaton to M90 +10% and +0% ndcate the ncrease n probabltes for mortalty and lfespan n relaton to M90 ************************************************************ Appendx The followng lst was compled from the reports ncluded n the Actuaral Report from
10 It ncludes reportng of longterm llness nsurance and premum exempton nsurance for all lfe nsurance companes excludng Alecta. Illness ncdence Run off Total Rato Results (rs premums  9% 4% 16% 13% (provsons for llness ncdence + IBNR)) / rs premums Result (actual run off estmated 61% 74% 81% 7% run off) / estmated run off Total result / revenue (rs premums 38% 5% 11% 6% + actual run off) The table shows that the assumptons regardng llness ncdence were sgnfcantly underestmated for the years 00 and 003. The values for 001 demonstrate an even greater underestmaton (but are not reported n the above table). Even f the run off shows postve results, the table shows that a stress test of llness ncdence should defntely be tested at a 50% level. Possble connectons to mproved run off shall not be assumed; rather the test level can be lowered. 10
Trafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
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