Fifth Quantitative Impact Study of Solvency II (QIS 5) National guidance on valuation of technical provisions for German SLT health insurance

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1 Fifh Quaniaive Impac Sudy of Solvency II (QIS 5) Naional guidance on valuaion of echnical provisions for German SLT healh insurance Conens 1 Inroducion Calculaion of bes-esimae provisions Rediscouned provision for increasing age Modifying he acuarial ineres rae as a resul of premium adusmen Revalued provision rofi sharing Bes-esimae provision Applicaion of shock scenarios Longeviy risk Moraliy risk Lapse risk Decrease in lapse raes Increase in lapse raes Mass lapse even Disabiliy/morbidiy risk Increase in income insurance benefi Increase in oher healh insurance benefis Reducion in insurance benefis for oher healh insurance Expense risk Model parameers... 23

2 1 Inroducion 1. German SLT healh insurance business includes a complex mechanism o adus he premiums depending on an iniiaing facor. The guidance ses ou how echnical provisions for such conracs could be deermined wih calculaion echniques similar o life aking such poenial for premium adusmens ino accoun. 2. Under Solvency II bes-esimae provisions are deermined hrough he valuaion of fuure cash flows. In he case of SLT healh insurance i may be assumed ha addiional cash ouflows owing o inflaion are compensaed by addiional inflows owing o premium adusmens. This is herefore a conservaive approach as addiional margins generaed by premium adusmens are no aken ino accoun. 3. This guidance oulines a possible mehod of implemening his approach wih regard o he deerminisic calculaion of bes-esimae provisions. The guidance has been coordinaed wih a working group of he German Acuarial Associaion (Deusche Akuarvereinigung DAV) he Associaion of rivae Healh Insurance Companies (Verb der privaen Krankenversicherung KV). The guidance is non-binding. 4. The guidance is required since he calculaion of echnical provisions for German SLT healh insurance conracs is very complicaed. This is due o premium adusmen clauses embedded in hese conracs as referred o above which allow he insurer o change he level of premiums under cerain pre-specified condiions. This is a produc ype specific for he German marke where guidance on he valuaion of echnical provisions is necessary o ensure a consisen reamen under QIS5 also o ensure ha he applicaion of he QIS5 specificaions is echnically feasible for all healh insurance underakings. 5. The guidance is consisen wih he Level 1 ex he QIS5 specificaions since i ses ou a valuaion of echnical provisions for German SLT healh insurance conracs which adequaely reflecs he economic effecs of claims inflaion premium adusmen clauses on he cash flows relaed o such conracs in line wih he general valuaion principles of he Solvency II framework. 6. This documen begins by seing ou how bes-esimae provisions can be calculaed. I hen shows how individual shock scenarios can be worked hrough using he model. 7. As wih he previous impac sudies he Federal Financial Supervisory Auhoriy (Bundesansal für Finanzdiensleisungsaufsich BaFin) will provide assisance in carrying ou he calculaions. 8. The model parameers which are used purely as variables in his documen are lised on page 23.

3 2 Calculaion of bes-esimae provisions 9. In his secion bes-esimae provisions are calculaed in several sages. Firsly he cash flows under he rules of he German Commercial Code (Helsgesezbuch ) are rediscouned (rediscouned provision for increasing age). A change in he acuarial ineres rae can be refleced as par of a premium adusmen. In addiion o invesmen surplus he nex sage involves allowing for oher underwriing surplus in he cash flow (revalued provision for increasing age). Then he policyholders fuure profi sharing is deermined. The bes-esimae provision is he sum of he revalued provision for increasing age policyholders fuure profi sharing. This procedure is referred o as inflaion-neural valuaion. 2.1 Rediscouned provision for increasing age 10. The rediscouned provision for increasing age NDR is calculaed as follows aking ino accoun a poenial premium adusmen o reduce he acuarial ineres rae: NDR = m N 1 + = 0 + ( 1 + i ) = N( 1 i ) where m undiscouned cash flow in year as per provision for increasing age according o (i.e. cash flow due o acuarial assumpions) undiscouned modified cash flow in year as per provision for increasing age wih acuarial ineres rae modified afer premium adusmen in year N N ime of premium adusmen (eiher or N ins ) i ineres rae for ime deriving from he risk-free ineres rae erm srucure 11. In order o be able o ake accoun of differing bonus raes for wo differen ime periods NDR is o be divided beween he ime periods [0k[ [k] for furher calculaions. 1 I should be noed ha k = N ins for QIS 5: NDR [ 0k [ k = + = 1 0 ( 1 i ) NDR = NDR NDR 0 [ k ] [ k [ 12. In order o calculae fuure discreionary benefis in he following i will also be necessary o consider he difference beween he marke value of 1 Differen bonus raes are required for differen ime periods because of he ime-limied impac of he shock scenarios.

4 he asses of he insurer he value of he asses under local. These differences are referred o as hidden reserves are denoed by R. 2 They mus also be divided beween he ime periods [0k[ [k] are hen denoed by R [0k[ R [k]. 13. If i is no possible o allocae he hidden reserves precisely o he wo ime periods i should be assumed conservaively ha he whole of he reserves are aribuable o he second period. 14. ro raa hidden reserves (posiive negaive) refer o he absolue share of he hidden reserves in he invesmen porfolio of SLT business which is aribuable o underwriing commimens. 3 These pro raa reserves are denoed by R a wih assignmen o he ime periods again denoed by he suffixes [0k[ [k]. 2.2 Modifying he acuarial ineres rae as a resul of premium adusmen 15. The iming of a planned adusmen o he acuarial ineres rae N ins is he sum of he ime unil he decision o adus he acuarial ineres rae he average waiing period unil he ineres rae is modified. 16. A premium adusmen wih regard o he ineres rae should be applied if such a change is likely in fuure in he ligh of he curren ineres rae siuaion invesmen porfolio fuure corporae planning he curren scenario. 17. When deciding o make premium adusmens a disincion should be made beween ariffs if here are maerial differences e.g. wih regard o he acuarial ineres rae or cash flows. 18. Because in SLT healh each parameer mus be based on conservaive esimaes in accordance wih secion 2 of he Calculaion Regulaion (Kalkulaionsverordnung KalV) in he case of he ineres rae parameer an average annual minimum ineres margin (i Marge ) can be assumed. 2 We noe ha he deerminaion of hidden reserves is necessary for he purpose of explaining how o calculae fuure discreionary benefis under German Healh SLT conracs since according o he legal condiions of hese conracs he policyholders profi sharing is based on he surpluses arising in he balance shee. Also noe ha posiive negaive reserves are need off ( he value of R may be posiive or negaive). 3 The saring poin for apporioning he reserves may be he curren echnical provisions: if for insance he value of he invesmen porfolio according o is 100 he value of underwriing commimens (provision for increasing age including direc crediing funds from sauory loading provision for premium refunds unearned premium reserves claims provision) according o is 90 hen he pro raa value of he hidden reserves is 90% of oal hidden reserves.

5 19. The acuarial ineres rae 4 should no be reduced if he presen value of maximum realizable fuure invesmen surplus excluding he premium adusmen a ime N ins V NDR + R Nins BA Nins a Nins is higher han he minimum invesmen surplus 20. Therefore V N ins = = N N ( 1 + i ) ( 1 + R ) N N M N. ins denoes he provision for increasing age according o excluding enilemens o premium reducion in old age (provision resuling from sauory loading direc crediing) in N ins years valued a ime 0 BA NDR N ins = = N ( + ) 1 i denoes he rediscouned provision for increasing age wihou a reducion in he acuarial ineres rae in N ins years valued a ime 0 a N R N ins = [ ] ( ) 1 ins a a min R k ;max R + VN V0 ; 0 = 0 ins 1 + i denoes he value of he remaining pro raa hidden reserves in N ins years valued a ime 0 (see subsecion 21) R denoes he acuarial ineres rae of he provision for increasing age wihou an adusmen of he acuarial ineres rae M N ins 1 = ( ) ( ) ( ) N ins Nins Nins + = ins + = N M arg e 1 i N ins N 1 R 1 + R + i ins denoes he presen value of he minimum invesmen surplus wihou an adusmen of he acuarial ineres rae valued a ime 0. 4 As almos all healh insurers currenly sill use he maximum acuarial ineres rae he model has principally been designed wih hese insurers in mind. However he model can also be used for increases in he acuarial ineres rae. An increase should no be applied if he presen value of he maximum realizable fuure invesmen surplus V NDR + R is less han he minimum invesmen surplus disregarding he premium adusmen. In he even of an adusmen he esimae for minimum invesmen surplus is o be revised upwards as appropriae. I mus also be borne in mind ha he acuarial ineres rae may no be raised higher han he maximum acuarial ineres rae. This scenario will no have any pracical relevance for QIS 5 which is why he model does no ye ake his scenario ino consideraion.

6 21. The formula N 1 ins = 0 1 ( + i ) + V Nins V 0 gives he ineres losses in he firs N ins years wihou reserves aken ino accoun. When deermining he remaining pro raa reserves he fac ha an insurer will wherever possible finance he acuarial ineres rae by realising hidden reserves if he risk-free ineres rae falls below he acuarial ineres rae is aken ino consideraion. 5 The formula akes accoun of he fac ha pro raa hidden reserves may no be sufficien for ha purpose. 22. If i is assumed ha he ineres rae is no changed in one of he subsequen premium adusmens hen he equaion N = +1 mus be se such ha he second sum in he calculaion of NDR in subsecion 10 disappears. In his case NDR can be calculaed direcly he nex few subsecions can be ignored wih he calculaion coninuing a subsecion Where a premium adusmen is being applied a realisic esimae is o be made of he discoun rae in he ligh of he curren ineres rae siuaion he curren invesmen porfolio fuure corporae planning in paricular. The acuarial ineres rae is o be applied in he model such ha for N := N ins he presen value of he maximum realizable fuure invesmen surplus V N NDR N + R a N equaes o he approximaion of minimum invesmen surplus M N. Therefore NDR N = m = N ( 1 + i ) denoes he rediscouned provision for increasing age in N years valued a ime 0 M N 1 = = M N ( ) ( ) ( ) N N N + = N + = N M arg e 1 in 1 R 1 + R + i denoes he approximaion of he presen value of he minimum invesmen surplus afer adusmen o he acuarial ineres rae valued a ime Therefore 5 In fac he risk-free ineres rae is no earned in pracice as he iniial invesmen income is based on he invesmens acually held. This is modelled by he risk-free ineres rae he holdings of posiive or negaive reserves. 6 I can be shown ha M N is less han he presen value of he minimum invesmen surplus wih acuarial ineres rae adusmen. Invesmen surplus is herefore esimaed conservaively.

7 NDR = = = N 1 = 0 N 1 = 0 N 1 = 0 is applied. ( 1 + i ) = N ( 1 + i ) ( 1 + i ) ( 1 + i ) + + NDR + V N m N + R a N M N 2.3 Revalued provision 25. The revalued provision for increasing age is he rediscouned provision for increasing age minus he discouned fuure oher echnical surplus: NBR = NDR [ 0k [ [ 0k [ k 1 = 0 + vü ( 1 i ) NBR = NDR [ k ] [ k ] = k vü ( 1 + i ) where vü undiscouned cash flow of bes-esimae underwriing surplus (excluding invesmen surplus). 26. vü can herefore be esimaed as follows: vü = rel min vü vü { rel } for < M oherwise where 6 werg3s s = 2 5 vü KapErgs rel = s werg3 s KapErg s s M inerim profi 3 as per saemen 231 for year s for SLT healh business invesmen surplus as per saemen 231 for year s for SLT healh business premiums 7 for year s for SLT healh business period over which he underwriing surplus (excluding invesmen surplus) is aken ino consideraion 8 7 The premiums should correspond o hose used in. The Excel calculaion guide assumes ha here is no difference in he consideraion (explici or implici) of coss.

8 2.4 rofi sharing 27. In addiion o he fuure realised surplus he value of he fuure discreionary benefis includes he non-commied share of he provision for premium refunds (RfB) ha is expeced o be paid ou o curren policyholders. Togeher wih he remaining fuure discreionary benefis his share of he RfB (hereafer referred o as rmrfb) conribues o he loss absorbing capaciy of he echnical provisions when deermining he SCR. rmrfb is derived as follows: rmrfb = RfB gebrfb where RfB gebrfb provision for premium refunds commied share of he RfB 28. The commied share of RfB comprises he wihdrawal amouns ha are ied up for subsequen financial years as defined in secion 21 (2) senence 2 no. 3 of he German Corporaion Tax Ac. (Körperschafseuergesez KSG). These include amouns aken ou wih regard o premium reducion easing of premium adusmens financing of addiional premiums in connecion wih increased benefis premium refunds. 29. Before calculaing he surplus i should firs be noed ha o cover invesmen losses he original division of reserves beween he periods [0k[ [k] may have o be aboned (see subsecion 21.). Therefore he values R a R pro raa hidden reserves (posiive negaive reserves are need off) oal hidden need of reserves o be apporioned o SLT business mus be modified as follows: R R ' R R k a a a = R = min R ;max R = [ ] [ k ] ( ) + V V k i 1 a' k k ; 0 0 a' = a a a' R + R 0 0 R [ k [ [ k [ [ k ] [ k ] a a' = R R + R [ k ] [ k ] [ k ] [ k ] ' = ' R + R 0 0 R. [ k [ [ k [ [ k ] [ k ] 30. Because of legal rules a disincion mus be made beween he invesmen surplus he overall surplus when modelling he profi sharing. 8 In order o achieve beer comparabiliy of he valuaions so as o be conservaive as regards he balance-shee proecion he oher underwriing surplus is only aken ino consideraion for a limied period.

9 Ü = 0 Ü ' 0 V V NBR + R [ k [ 0 k [ 0k [ [ k [ ' = V NBR + R [ k ] k [ k ] [ k ] Ü = 0 Ü ins a' 0 V V NDR + R [ k [ 0 k [ 0k [ [ k [ ins a' = V NDR + R [ k ] k [ k ] [ k ] where for he individual periods: Ü Ü ins V k presen value of fuure surplus (according o ) presen value of fuure invesmen surplus (according o ) denoes he provision for increasing age under excluding enilemens o premium reducion in old age (provision resuling from sauory loading direc crediing) in k years valued a ime 0 (see subsecion 21.) NDR rediscouned provision for increasing age (see subsecions ) NBR revalued provision for increasing age (see subsecion 25.). 31. Surpluses from provisions arising from sauory loading direc crediing can only be modelled if hese provisions can be proeced for he fuure. This requires he premium adusmens o be applied in more deail. As a conservaive esimae i is herefore assumed ha insurers do no receive a share of he surplus from hese provisions. The profi sharing is no however shown separaely here bu is implicily conained in NBR. 32. For he individual periods [0k[ [k] we hen se ÜB ins ins ins { BS Ü ;0} = max where ÜB ins BS ins Ü ins curren value of policyholders fuure invesmen profi sharing 9 invesmen bonus rae (see secion 12a of he Insurance Supervision Ac (Versicherungsaufsichsgesez - VAG)) presen value of fuure invesmen surplus (under rules); see subsecion Also for he individual periods [0k[ [k] we se ÜB ins ins { BS Ü ÜB ;0} + v ins = ÜB + max where ÜB ins+v presen value of policyholders fuure profi sharing aribuable o invesmen underwriing 9 In QIS 5 he profi sharing is defined as he value of he benefis payable o policyholders in addiion o he guaraneed benefis.

10 BS Ü bonus rae presen value of fuure surplus (under rules) see subsecion The bonus raes in subsecions should be seleced on he basis of he bes-esimae average noing ha hey relae o he oal periods [0k[ [k]. Shor-erm falls in he profi sharing e.g. following a shock scenario should herefore have only an exremely limied impac on he bonus rae o be applied o period [k]. 35. If differen bonus raes are expeced beween ariffs (e.g. as regards nonprofi-relaed premium refunds in he case of group insurance conracs or owing o he fac ha secion 12 (a) VAG only applies o medical expenses volunary long-erm care insurance) hen a disincion should be made beween he ariffs. = { + { ; 0} 0} ; ins + V ins + V ins 36. ÜB ÜB[ k [ ÜB[ k ] max rmrfb min Ü[ 0k [ ÜB[ 0k [ where ÜB is he presen value of policyholders fuure profi sharing. 37. The above formula adds he erm rmrfb o ÜB ins+v only insofar as his is no used o balance shorfalls resuling from invesmen underwriing. The limiaion of rmrfb corresponds o he use of RfB funds o aver an emergency siuaion as described in secion 56a VAG. This limiaion should only be relevan if ÜB is recalculaed o deermine a ne SCR. If he reducion of rmrfb does no appear reasonable in view of he level of he oal SCR because he insurance underaking is expeced o bear a (greaer) share of he losses iself hen he (maximum) reducion should no be applied Bes-esimae provision 38. EWR = NBR + ÜB + RsE + BÜ + RsVF + gebrfb + sonsr where: EWR NBR ÜB RsE bes-esimae provision revalued provision for increasing age under curren value of policyholders fuure profi sharing provisions for enilemens o premium reducion in 10 The formula herefore assumes ha if a 200-year loss occurs (arge value for he SCR calibraion) he uncommied RfB funds will be uilised o offse losses as per secion 56a VAG. The formulae for deermining ÜB also assume ha profis losses can be offse for differen financial years which may no necessarily be he case. Conversely he value of RfB under rules is reaed as a liabiliy in he formula even hough he invesmen income arising from he RfB is only parially included in he profi sharing which would acually reduce he value of he liabiliy. The above needs o be borne in mind when inerpreing he resuls.

11 old age under (provision for sauory loading direc crediing) BÜ RsVF gebrfb sonsr unearned premium provisions under provision for claims incurred under commied share of he RfB oher echnical provisions under

12 3 Applicaion of shock scenarios 39. The subsecions below describe how he underwriing risk scenarios are applied wih inflaion-neural valuaion. 40. In his discussion i ( NAV S) describes he effec of shock S on he difference beween asses liabiliies wihou a change in he fuure profi sharing. 41. Similarly i ( NAV S) denoes he impac of shock S on he difference beween asses liabiliies wih a change in he fuure profi sharing based on he scenario. 42. For inflaion-neural valuaion he impac of he shocks wihou risk miigaion hrough profi sharing described on he following pages is given by 11 where i ( NAV S) = NBR S NBR S NBR S = revalued provision for increasing age for ariff group wihou shock NBR S = revalued provision for increasing age for ariff group under shock S. 43. For he impac of he shocks wih risk miigaion hrough a change in he profi sharing 11 i ( nnav S) = EWR S EWR S applies where EWR S = bes-esimae provision for ariff group wihou shock EWR S = bes-esimae provision for ariff group under shock S. 44. If here is reinsurance cover any change in he reinsurance receivables also needs o be included in he above calculaions. 11 The asses are assumed o remain unchanged in he underwriing risk scenarios.

13 3.1 Longeviy risk 45. For he longeviy shock a permanen 20% reducion in moraliy raes is assumed where a decrease in he moraliy rae leads o an increase in he value of he echnical provisions. 46. In inflaion-neural valuaion he impac of he shock on he fuure surplus is considered for he period up o adusmen o he longeviy shock N qx. I is assumed hereafer ha he shock is neuralised by a premium adusmen. There are herefore no addiional margins hrough rising premiums for he duraion of he calculaion. 47. The balance-shee provision for increasing age for a policyholder is given by he following equaion where he provision is revalued annually: where + 1 ( V + K ) ( 1 + R) = ( 1 q w ) V x( ) x( ) x( ) i V provision for increasing age for policyholder in year (wihou shock) ne premium for policyholder in year R acuarial ineres rae x() age of policyholder in year K x acuarial per capia claim for age x q x acuarial moraliy rae for age x w x acuarial lapse probabiliy for age x. 48. A he end of year acuarial funds of + 1 ( 1 q w ) V x( ) x( ) are available for every policyholder for forming he fuure provision. However in he even of deviaion from moraliy by a facor (1 + a) funds amouning o + 1 ( 1 q ( 1 + a) w ) V x( ) x( ) are needed. Thus his change in moraliy has he following effec on he resul a he end of year :

14 ( 1 q w ) ( 1 q ( 1 + a) w ) V = a q V x( ) x( ) x( ) x( ) x( ) 49. For he sake of simpliciy i can be assumed ha he change in moraliy in he shock scenario relaes o acuarial moraliy. However if he daa is available he acual moraliy figure can be used insead. For he resuling weighed moraliy q for he whole porfolio for all 0 < N qx he equaion q x (i ) V + 1 q V + 1 should approximaely hold good. 50. For he shock where a = 20% he bes-esimae underwriing surplus for < N qx is replaced by. vü = rel vü 20% q V 1 + i + 1 where i ineres rae o erm resuling from he risk-free ineres rae erm srucure V provision for increasing age for porion of he porfolio under consideraion a ime 51. Addiional income resuling from a longer say in he pool is disregarded for he sake of simpliciy. SLT SLT 52. The capial charges Healh longeviy nhealh longeviy can hen be derived direcly from i ( NAV longeviy) i ( nnav longeviy). 3.2 Moraliy risk 53. The moraliy shock assumes a permanen 15% increase in moraliy where an increase in he moraliy rae leads o an increase in he value of he echnical provisions. 54. The echnical specificaions for QIS 5 (see SCR.8.19.) require ha he risk of loss of fuure income hrough he early deah of policyholders is considered for inflaion-neural valuaion. As he underwriing surplus vü in subsecion 26. is calculaed on he basis of fuure premiums he effec of he shock can be calculaed hrough he fall in premiums. 55. I is also needs o be borne in mind ha unil premiums are adused o he higher moraliy raes he surplus will change due o addiional inheriance which are aken ino accoun by modifying vü.

15 SLT SLT 56. The capial charges Healh moraliy nhealh moraliy can hen be derived direcly from i ( NAV moraliy) i ( nnav moraliy). 57. If (1 q w ) represens he average annual probabiliy of saying in he pool in year before he shock hen he average porfolio size for = 0 o changes by he facor f moraliy = ( 1 115% q' w' ) ( q w ) ' = 0 1 ' ' where q denoes he average probabiliy of moraliy in year w denoes he average lapse probabiliy in year. 58. The values for q w are o be ascerained on an underaking-specific basis for = 0. The subsequen values are deermined in one-year seps on he basis of curren probabiliy ables average annual porfolio ageing of 1 year. 59. N qxup denoes he period unil premiums are adused in line wih he increased moraliy rae. Loss resuling from reducion of premiums 60. For he period unil premium adusmen ( < N qxup ) where denoes premiums as per cash flow we obain he new premium resuling from he moraliy shock from moraliy = f moraliy by muliplying he change in he porfolio by he old premium. 61. From N qxup he premium adusmen resuling from he changed moraliy rae mus also be aken ino accoun. The new premium is se such ha he equaion = Nqxup f moraliy Nqxup ( 1 + R) L ( 1 + i ) Nqxup Nqxup f moraliy V Nqxup = = Nqxup moraliy Nqxup ( 1 + R) where L denoes payous as per cash flow V N qx as in subsecion 20.

16 holds good. 62. Therefore for N qxup moraliy = s = Nqxup f moraliy s L ( 1 + R) moraliy s s Nqxup s= Nqxup ( 1 + i ) Nqxup ( 1 + R) Nqxup s s Nqxup f moraliy s V Nqxup is se as an approximaion. 63. The annual loss from he moraliy shock amouning o moraliy vü ( ) rel is calculaed by replacing in he calculaion of vü in subsecion 26. wih. moraliy Change of surplus resuling from addiional inheriance 64. In he firs N qxup years unil premiums are adused in line wih he increased moraliy rae addiional surpluses arise (analogously o subsecions 47. o 50. bu wih a = +15%) amouning o 15% q f moraliy 1 + i V + 1 which in addiion o he operaion in subsecion 63 can be applied direcly o increase v. 3.3 Lapse risk 65. For QIS 5 he lapse risk for SLT healh insurance is ascerained for boh an increase a decrease in he lapse raes. The capial charges Healh SLT nhealh lapse are derived from max max Decrease in lapse raes { i( NAV Lapseup ); i( NAV Lapse ); ( NAV Lapse )} i mass SLT lapse { i( nnav Lapseup ); i( nnav Lapse ); ( nnav Lapse )} i mass 66. A permanen 20% decrease in lapses is assumed for he shock for all policies ha are adversely affeced by such risk.

17 67. For he inflaion-neural valuaion he impac of he shock on he fuure surplus is calculaed for he period up o adusmen o he decrease in lapse raes N wx. 68. I is o be assumed for he sake of simpliciy ha he change in he lapse raes in he shock scenario relaes o he acuarial lapse raes. However if he daa is available he acual lapse raes can be used insead. For he resuling weighed lapse probabiliy w for he whole porfolio for all 0 < N wx he equaion w x (i ) V + 1 w V + 1 should approximaely hold good. 69. Analogously o subsecions 47. o 50. for he decrease in lapse raes he bes-esimae underwriing surplus is replaced in he inflaion-neural valuaion by vü = rel vü 20% w V 1 + i + 1 for < N wx. 70. Addiional income resuling from a longer say in he pool is disregarded for he sake of simpliciy Increase in lapse raes 71. A permanen 20% increase in lapses is assumed for he shock for all policies ha are adversely affeced by such risk. 72. If (1 q w ) represens he average annual probabiliy of saying in he pool in year before he shock hen he average porfolio size for = 0 o changes by he facor f lapseup = ( 1 q' 120% w' ) ( q w ) ' = 0 1 ' ' where he probabiliy of moraliy q he lapse probabiliy w are ascerained as in subsecion Below N wxup denoes he period unil premiums are adused in line wih he increased lapses. Loss resuling from reducion of premiums 74. As wih he moraliy shock we obain he new premium resuling from he increase in he lapse raes lapseup = f for < N wxup lapseup

18 lapseup = s = Nwxup f lapseup s L ( 1 + R ) lapseup s s Nwxup s= Nwxup ( 1 + i ) Nwxup ( 1 + R ) Nwxup s s Nwxup f lapseup s V Nwxup oherwise 75. The annual loss from he increase in lapse raes amouning o lapseup vü ( ) rel is calculaed by replacing in he calculaion of vü in subsecion 26. wih. lapseup Change of surplus resuling from addiional inheriance 76. In he firs N qxup years unil premiums are adused in line wih he increased lapse rae surpluses arise (analogously o subsecions 47. o 50. bu wih a = +20%) amouning o 20% w f lapseup 1 + i V + 1 which in addiion o he operaion in subsecion 75. can be applied direcly o increase v Mass lapse even 77. The shock assumes ha for one ime 30% of he policies will be cancelled ha are affeced adversely by such risk. 78. The average porfolio size changes by he consan facor f lapsemass ( 1 q0 30% ) ( 1 q w ) = 0 0 where he probabiliy of moraliy q 0 he lapse probabiliy w 0 are ascerained as in subsecion 58. Loss resuling from reducion of premiums 79. As he shock occurs only for one year in conras o he moraliy shock he increase in lapse raes no premium adusmen is necessary. So he new premiums resul from lapsemass = f. lapsemass

19 80. The annual loss from he increase in lapse raes amouning o lapsemass vü ( ) rel is calculaed by replacing in he calculaion of vü in subsecion 26. wih. lapsemass Change of surplus resuling from addiional inheriance 81. In he firs year surplus arise (analogously o subsecions 76) amouning o ( 30% w ) i V + 1 which in addiion o he operaion in subsecion 80. can be applied direcly o increase v. 3.4 Disabiliy/morbidiy risk 82. For QIS 5 a disincion is drawn beween income proecion insurance SLT oher ypes of healh insurance. The capial charges Healh nhealh are derived from he sum of SLT disabbiliy / morbidiy disabbiliy / morbidiy i ( NAV oher healh insurance) + i ( NAV income insurance) i ( nnav oher healh insurance) + i ( nnav income insurance). 83. In addiion a disincion needs o be drawn beween he shocks resuling from an increase a decrease in benefis for oher healh insurance. If S up S denoe hese shock scenarios hen we obain i ( nnav S) = max{ i ( nnav S up ); i ( nnav S ) i ( NAV S) = up up i( NAV S ) if i( nnav S ) > i( nnav S ) up i( NAV S ) if i( nnav S ) < i( nnav S ) up { i( NAV S ); i( NAV S )} oherwise. max 84. The period up unil premiums can be adused o neuralise he effecs of he shock is denoed by N VL Increase in income insurance benefi 85. The shock assumes a 50% increase in payous for income insurance in he firs year an increase of 25% in all subsequen years.

20 86. This means ha using he benefi paymens L defined in he cashflow he bes-esimae underwriing surplus for he ime poins < N VL is replaced by vü = rel vü φsq L 50% falls = 0 25% sons where φ SQ indicaes he average raio of he paid he calculaed insurance benefis for income insurance for he las five years. If no separae daa is available for income insurance benefi hen he daa is o be esimaed by an appropriae mehod. If daa for five years is no available hen we se φsq = 1. The firs hree years afer esablishmen of he underaking can be disregarded Increase in oher healh insurance benefis 87. The shock for oher healh insurance assumes a one-off 5% increase in insurance benefis a 1 percenage poin rise in annual medical inflaion. 88. This means ha using he benefi paymens L defined in he cash flow he bes-esimae underwriing surplus for he ime poins < N VL is replaced by where vü vü = rel + φsq L (1 (1 + 1%) (1 + 5%)) φ SQ indicaes he average raio of he paid he calculaed insurance benefis for oher healh insurance for he las five years. If no separae daa is available for oher healh insurance hen he daa is o be esimaed by an appropriae mehod. If daa for five years is no available hen we se φsq = 1. The firs hree years afer esablishmen of he underaking can be disregarded.

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