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Fifth Quantitative Impact Study of Solvency II (QIS 5)

National guidance on valuation of technical provisions for German SLT health insurance

Contents

1 Introduction ... 2

2 Calculation of best-estimate provisions ... 3

2.1 Rediscounted provision for increasing age ... 3

2.2 Modifying the actuarial interest rate as a result of premium adjustment 4 2.3 Revalued provision ... 7

2.4 Profit sharing ... 8

2.5 Best-estimate provision ... 10

3 Application of shock scenarios... 12

3.1 Longevity risk ... 13

3.2 Mortality risk ... 14

3.3 Lapse risk ... 16

3.3.1 Decrease in lapse rates ... 16

3.3.2 Increase in lapse rates... 17

3.3.3 Mass lapse event... 18

3.4 Disability/morbidity risk ... 19

3.4.1 Increase in income insurance benefit ... 19

3.4.2 Increase in other health insurance benefits ... 20

3.4.3 Reduction in insurance benefits for other health insurance ... 21

3.5 Expense risk ... 22

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1 Introduction

1. German SLT health insurance business includes a complex mechanism to adjust the premiums depending on an initiating factor. The guidance sets out how technical provisions for such contracts could be determined with calculation techniques similar to life taking such potential for premium adjustments into account.

2. Under Solvency II, best-estimate provisions are determined through the valuation of future cash flows. In the case of SLT health insurance, it may be assumed that additional cash outflows owing to inflation are

compensated by additional inflows owing to premium adjustments. This is therefore a conservative approach, as additional margins generated by premium adjustments are not taken into account.

3. This guidance outlines a possible method of implementing this approach with regard to the deterministic calculation of best-estimate provisions. The guidance has been coordinated with a working group of the German

Actuarial Association (Deutsche Aktuarvereinigung – DAV) and the

Association of Private Health Insurance Companies (Verband der privaten Krankenversicherung – PKV). The guidance is non-binding.

4. The guidance is required since the calculation of technical provisions for German SLT health insurance contracts is very complicated. This is due to premium adjustment clauses embedded in these contracts as referred to above, which allow the insurer to change the level of premiums under certain pre-specified conditions. This is a product type specific for the German market where guidance on the valuation of technical provisions is necessary to ensure a consistent treatment under QIS5 and also to ensure that the application of the QIS5 specifications is technically feasible for all health insurance undertakings.

5. The guidance is consistent with the Level 1 text and the QIS5 specifications since it sets out a valuation of technical provisions for German SLT health insurance contracts which adequately reflects the economic effects of claims inflation and premium adjustment clauses on the cash flows related to such contracts in line with the general valuation principles of the

Solvency II framework.

6. This document begins by setting out how best-estimate provisions can be calculated. It then shows how individual shock scenarios can be worked through using the model.

7. As with the previous impact studies, the Federal Financial Supervisory Authority (Bundesanstalt für Finanzdienstleistungsaufsicht – BaFin) will provide assistance in carrying out the calculations.

8. The model parameters which are used purely as variables in this document are listed on page 23.

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2 Calculation of best-estimate provisions

9. In this section best-estimate provisions are calculated in several stages. Firstly, the cash flows under the rules of the German Commercial Code (Handelsgesetzbuch – HGB) are rediscounted (rediscounted provision for increasing age). A change in the actuarial interest rate can be reflected as part of a premium adjustment. In addition to investment surplus, the next stage involves allowing for other underwriting surplus in the cash flow (revalued provision for increasing age). Then the policyholders’ future profit sharing is determined. The best-estimate provision is the sum of the

revalued provision for increasing age and policyholders’ future profit sharing. This procedure is referred to as inflation-neutral valuation.

2.1 Rediscounted provision for increasing age

10. The rediscounted provision for increasing age NDR is calculated as follows, taking into account a potential premium adjustment to reduce the actuarial interest rate:

(

)

(

)

∑ ω = − = + + + = N t t t HGB t N t t t HGB t i mZ i Z NDR 1 1 1 0 , where

ZtHGB undiscounted cash flow in year t as per provision for increasing age according to HGB (i.e. cash flow due to actuarial assumptions)

mZtHGB undiscounted modified cash flow in year t as per HGB provision for increasing age with actuarial interest rate modified after premium adjustment in year N

N time of premium adjustment (either ω or NZins)

it interest rate for time t deriving from the risk-free interest rate term structure

11. In order to be able to take account of differing bonus rates for two different time periods, NDR is to be divided between the time periods [0,k[ and [k,ω] for further calculations.1 It should be noted that k = NZins for QIS 5:

[ [

(

)

∑− = + = 1 0 0 1 k t t t HGB t k , i Z NDR [k, ] NDR NDR[ ,k[ NDR ω = − 0

12. In order to calculate future discretionary benefits, in the following it will also be necessary to consider the difference between the market value of

1 Different bonus rates are required for different time periods because of the time-limited impact of

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the assets of the insurer and the value of the assets under local HGB. These differences are referred to as “hidden reserves” and are denoted by R.2 They must also be divided between the time periods [0,k[ and [k,ω] and are then denoted by R[0,k[ and R[k,ω].

13. If it is not possible to allocate the hidden reserves precisely to the two time periods, it should be assumed conservatively that the whole of the reserves are attributable to the second period.

14. Pro rata hidden reserves (positive and negative) refer to the absolute share of the hidden reserves in the investment portfolio of SLT business which is attributable to underwriting commitments.3 These pro rata reserves are denoted by Ra, with assignment to the time periods again denoted by the suffixes [0,k[ and [k,ω].

2.2 Modifying the actuarial interest rate as a result of premium adjustment 15. The timing of a planned adjustment to the actuarial interest rate NZins is the

sum of the time until the decision to adjust the actuarial interest rate and the average waiting period until the interest rate is modified.

16. A premium adjustment with regard to the interest rate should be applied if such a change is likely in future in the light of the current interest rate situation, investment portfolio, future corporate planning and the current scenario.

17. When deciding to make premium adjustments, a distinction should be made between tariffs if there are material differences, e.g. with regard to the actuarial interest rate or cash flows.

18. Because in SLT health each parameter must be based on conservative estimates, in accordance with section 2 of the Calculation Regulation

(Kalkulationsverordnung – KalV), in the case of the interest rate parameter an average annual minimum interest margin (iMarge) can be assumed.

2 We note that the determination of “hidden reserves” is necessary for the purpose of explaining

how to calculate future discretionary benefits under German Health SLT contracts since according to the legal conditions of these contracts the policyholders’ profit sharing is based on the surpluses arising in the HGB balance sheet. Also note that positive and negative reserves are netted off (and the value of R may be positive or negative).

3

The starting point for apportioning the reserves may be the current HGB technical provisions: if, for instance, the value of the investment portfolio according to HGB is 100 and the value of underwriting commitments (provision for increasing age including direct crediting and funds from statutory loading, provision for premium refunds, unearned premium reserves, claims provision) according to HGB is 90, then the pro rata value of the hidden reserves is 90% of total hidden reserves.

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19. The actuarial interest rate4 should not be reduced if the present value of maximum realizable future investment surplus excluding the premium adjustment, at time NZins

a

N BAP N

NZins NDR Zins R Zins

V − ¬ +

is higher than the minimum investment surplus

Zins N ZM . 20. Therefore, Zins N V =

(

) (

)

∑ω =N + ⋅ + − t N t N N HGB t RZ i Z 1 1 ,

denotes the provision for increasing age according to HGB,

excluding entitlements to premium reduction in old age (provision resulting from statutory loading and direct crediting) in NZins years, valued at time 0, BAP NZins NDR¬ =

(

)

∑ω =N + t t t HGB t i Z 1 ,

denotes the rediscounted provision for increasing age, without a reduction in the actuarial interest rate in NZins years, valued at time 0, a NZins R = [ ]

(

)

                        − + + − ∑− = ω 0 1 0 1 0 ; V V i Z R max ; R

min NZins NZins

t t t HGB t a a , k ,

denotes the value of the remaining pro rata hidden reserves in NZins years, valued at time 0 (see subsection 21),

RZ denotes the actuarial interest rate of the HGB provision for

increasing age without an adjustment of the actuarial interest rate, and Zins N ZM

(

)

(

)

(

)

       + + − + + = ∑ ∑ω = − ω

= Zins − Zins Zins Zins

Zins Zins N t Marge t N HGB t N t t N HGB t N N RZ i Z RZ Z i 1 1 1 1

denotes the present value of the minimum investment surplus without an adjustment of the actuarial interest rate, valued at time 0.

4 As almost all health insurers currently still use the maximum actuarial interest rate, the model

has principally been designed with these insurers in mind. However, the model can also be used for increases in the actuarial interest rate. An increase should not be applied if the present value of the maximum realizable future investment surplus V – NDR + R is less than the minimum investment surplus, disregarding the premium adjustment. In the event of an adjustment, the estimate for minimum investment surplus is to be revised upwards as appropriate. It must also be borne in mind that the actuarial interest rate may not be raised higher than the maximum actuarial interest rate.

This scenario will not have any practical relevance for QIS 5, which is why the model does not yet take this scenario into consideration.

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21. The formula

(

)

0 1 0 1 V V i Z Zins Zins N N t t t HGB t + + ∑− =

gives the interest losses in the first NZins years without reserves taken into account. When determining the remaining pro rata reserves, the fact that an insurer will, wherever possible, finance the actuarial interest rate by realising hidden reserves if the risk-free interest rate falls below the actuarial interest rate is taken into consideration.5 The formula takes account of the fact that pro rata hidden reserves may not be sufficient for that purpose.

22. If it is assumed that the interest rate is not changed in one of the

subsequent premium adjustments, then the equation N = ω+1 must be set such that the second sum in the calculation of NDR in subsection 10

disappears. In this case, NDR can be calculated directly and the next few subsections can be ignored, with the calculation continuing at subsection 25. 23. Where a premium adjustment is being applied, a realistic estimate is to be

made of the HGB discount rate in the light of the current interest rate situation, the current investment portfolio and future corporate planning in particular. The actuarial interest rate is to be applied in the model such that for N := NZins the present value of the maximum realizable future

investment surplus VN – NDRN + RaN equates to the approximation of minimum investment surplus ZMPN.

Therefore, NDRN = ∑ω =N + t t t HGB t ) i ( mZ 1 ,

denotes the rediscounted provision for increasing age in N years, valued at time 0, ZMPN

(

)

(

)

(

)

       + + − + + = = ∑ ∑ω = − ω = − t N Marge t N HGB t N t t N HGB t N N N i RZ Z RZ Z i ZM 1 1 1 1

denotes the approximation of the present value of the minimum investment surplus after adjustment to the actuarial interest rate, valued at time 06.

24. Therefore,

5 In fact the risk-free interest rate is not earned in practice, as the initial investment income is

based on the investments actually held. This is modelled by the risk-free interest rate and the holdings of positive or negative reserves.

6

It can be shown that ZMPN is less than the present value of the minimum investment surplus with

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(

)

(

)

(

)

(

)

N a N N N t t t HGB t N N t t t HGB t N t t t HGB t N t t t HGB t ZMP R V i Z NDR i Z i mZ i Z NDR − + + + = + + = + + + = ∑ ∑ ∑ ∑ − = − = ω = − = 1 0 1 0 1 0 1 1 1 1 is applied. 2.3 Revalued provision

25. The revalued provision for increasing age is the rediscounted provision for increasing age minus the discounted future other technical surplus:

[ [ [ [ ∑

(

)

− = + − = 1 0 0 0 1 k t t t vtÜ t k , k , i Z NDR NBR and [ ] [ ] ∑

(

)

ω = ω ω + − = k t t t vtÜ t , k , k i Z NDR NBR 1 , where

ZtvtÜ undiscounted cash flow of best-estimate underwriting surplus (excluding investment surplus).

26. ZtvtÜ can therefore be estimated as follows:

{

}

    ⋅ < ⋅ = otherwise , for , vtÜ t vtÜ t vtÜ t relZ P min M t relZ P Z , where

− − = ⋅ − = 6 2 5 3 s s s s vtÜ P KapErg ZwErg relZ and

ZwErg3s interim profit 3 as per statement 231 for year s for SLT health business

KapErgs investment surplus as per statement 231 for year s for SLT health business

Ps premiums7 for year s for SLT health business

M period over which the underwriting surplus (excluding investment surplus) is taken into consideration8

7 The premiums should correspond to those used in Z

tHGB. The Excel calculation guide assumes that

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2.4 Profit sharing

27. In addition to the future realised surplus, the value of the future

discretionary benefits includes the non-committed share of the provision for premium refunds (RfB) that is expected to be paid out to current

policyholders. Together with the remaining future discretionary benefits, this share of the RfB (hereafter referred to as rmRfB) contributes to the loss absorbing capacity of the technical provisions when determining the SCR. rmRfB is derived as follows:

rmRfB = RfB – gebRfB, where

RfB provision for premium refunds gebRfB committed share of the RfB

28. The committed share of RfB comprises the withdrawal amounts that are tied up for subsequent financial years as defined in section 21 (2) sentence 2 no. 3 of the German Corporation Tax Act. (Körperschaftsteuergesetz – KStG). These include amounts taken out with regard to premium reduction, easing of premium adjustments, financing of additional premiums in

connection with increased benefits and premium refunds.

29. Before calculating the surplus it should first be noted that to cover investment losses the original division of reserves between the periods [0,k[ and [k,ω] may have to be abandoned (see subsection 21.). Therefore, the values

Ra pro rata hidden reserves (positive and negative reserves are netted off)

R total hidden netted of reserves to be apportioned to SLT business must be modified as follows:

[ ] [ ]

(

)

                        − + + − = = ∑− = ω ω 0 1 0 1 0 k V V ; i Z R max ; R min R R k k t t t HGB t a a , k a ' a , k , [ [ [ [ [ ] [ak', ] a , k a k , ' a k , R R R R0 = 0 + ωω , [ ] [ ] [ ] [ak', ] a , k , k ' , k R R R R ω = ωω + ω and [ [ [ ,k[ [k, ] ['k, ] ' k , R R R R0 = 0 + ωω.

30. Because of legal rules, a distinction must be made between the investment surplus and the overall surplus when modelling the profit sharing.

8 In order to achieve better comparability of the valuations, and so as to be conservative as

regards the balance-sheet projection, the other underwriting surplus is only taken into consideration for a limited period.

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[ ,k[ V Vk NBR[ ,k[ R[' ,k[ ZÜ0 = 0 − − 0 + 0 , [k, ] Vk NBR[k, ] R'[k, ] ZÜ ω = − ω + ω, [ [ k [ ,k[ [a',k[ Zins k , V V NDR R ZÜ0 = 0 − − 0 + 0 and [ ] k [k, ] [ak', ] Zins , k V NDR R ZÜ ω = − ω + ω,

where, for the individual periods:

ZÜ present value of future surplus (according to HGB),

ZÜZins present value of future investment surplus (according to HGB), Vk denotes the provision for increasing age under HGB, excluding

entitlements to premium reduction in old age (provision resulting from statutory loading and direct crediting) in k years, valued at time 0 (see subsection 21.)

NDR rediscounted HGB provision for increasing age (see subsections 10. and 23.),

NBR revalued HGB provision for increasing age (see subsection 25.). 31. Surpluses from provisions arising from statutory loading and direct

crediting can only be modelled if these provisions can be projected for the future. This requires the premium adjustments to be applied in more detail. As a conservative estimate it is therefore assumed that insurers do not receive a share of the surplus from these provisions. The profit sharing is not, however, shown separately here, but is implicitly contained in NBR. 32. For the individual periods [0,k[ and [k,ω] we then set

{

BS ZÜ ;0

}

max

ZÜBZins Zins Zins

= , where

ZÜBZins current value of policyholders’ future investment profit sharing9

BSZins investment bonus rate (see section 12a of the Insurance Supervision Act (Versicherungsaufsichtsgesetz - VAG))

ZÜZins present value of future investment surplus (under HGB rules); see subsection 30.

33. Also for the individual periods [0,k[ and [k,ω] we set

{

BS ZÜ ZÜB ;0

}

max ZÜB

ZÜBZins+vt = Zins + Zins , where

ZÜBZins+vt present value of policyholders’ future profit sharing attributable to investment and underwriting

9 In QIS 5 the profit sharing is defined as the value of the benefits payable to policyholders in

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BS bonus rate

ZÜ present value of future surplus (under HGB rules), see subsection 30.

34. The bonus rates in subsections 32 and 33 should be selected on the basis of the best-estimate average, noting that they relate to the total periods [0,k[ and [k,ω]. Short-term falls in the profit sharing, e.g. following a shock scenario, should therefore have only an extremely limited impact on the bonus rate to be applied to period [k,ω].

35. If different bonus rates are expected between tariffs (e.g. as regards non-profit-related premium refunds in the case of group insurance contracts, or owing to the fact that section 12 (a) VAG only applies to medical expenses and voluntary long-term care insurance), then a distinction should be made between the tariffs.

36. ZÜB ZÜB[0 [ ZÜB[ ] max

{

rmRfB min

{

[0 [ ZÜB[Zins0 [;0

}

;0

}

k , k , Vt Zins , k Vt Zins k , + + + − = + ω + , where ZÜB is the present value of policyholders’ future profit sharing. 37. The above formula adds the term rmRfB to ZÜBZins+Vt only insofar as this is

not used to balance shortfalls resulting from investment and underwriting. The limitation of rmRfB corresponds to the use of RfB funds to avert an emergency situation as described in section 56a VAG. This limitation should only be relevant if ZÜB is recalculated to determine a net SCR. If the

reduction of rmRfB does not appear reasonable in view of the level of the total SCR because the insurance undertaking is expected to bear a

(greater) share of the losses itself, then the (maximum) reduction should not be applied.10

2.5 Best-estimate provision

38. EWR = NBR+ZÜB+RstPE +BÜ +RstVF +gebRfB+sonstR, where:

EWR best-estimate provision

NBR revalued provision for increasing age under HGB ZÜB current value of policyholders’ future profit sharing RstPE provisions for entitlements to premium reduction in

10 The formula therefore assumes that if a 200-year loss occurs (target value for the SCR

calibration), the uncommitted RfB funds will be utilised to offset losses as per section 56a VAG. The formulae for determining ZÜB also assume that profits and losses can be offset for different

financial years, which may not necessarily be the case. Conversely, the value of RfB under HGB rules is treated as a liability in the formula, even though the investment income arising from the RfB is only partially included in the profit sharing, which would actually reduce the value of the liability. The above needs to be borne in mind when interpreting the results.

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old age under HGB (provision for statutory loading and direct crediting)

BÜ unearned premium provisions under HGB RstVF provision for claims incurred under HGB gebRfB committed share of the RfB

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3 Application of shock scenarios

39. The subsections below describe how the underwriting risk scenarios are applied with inflation-neutral valuation.

40. In this discussion, ∑i (∆NAV|S)

describes the effect of shock S on the difference between assets and liabilities without a change in the future profit sharing.

41. Similarly,

∑i (∆NAV|S)

denotes the impact of shock S on the difference between assets and liabilities with a change in the future profit sharing based on the scenario. 42. For inflation-neutral valuation, the impact of the shocks without risk

mitigation through profit sharing described on the following pages is given by 11

∑i (∆NAV|S) = ∑j NBRjS – NBR¬jS, where

NBRj¬S = revalued provision for increasing age for tariff group j without shock

and

NBRjS = revalued provision for increasing age for tariff group j under shock S.

43. For the impact of the shocks with risk mitigation through a change in the profit sharing11

∑i (∆nNAV|S) = ∑j EWRjS – EWR¬jS, applies, where

EWRj¬S = best-estimate provision for tariff group j without shock and

EWRjS = best-estimate provision for tariff group j under shock S. 44. If there is reinsurance cover, any change in the reinsurance receivables

also needs to be included in the above calculations.

11

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3.1 Longevity risk

45. For the longevity shock, a permanent 20% reduction in mortality rates is assumed, where a decrease in the mortality rate leads to an increase in the value of the technical provisions.

46. In inflation-neutral valuation, the impact of the shock on the future surplus is considered for the period up to adjustment to the longevity shock Nqxdown. It is assumed thereafter that the shock is neutralised by a premium

adjustment. There are therefore no additional margins through rising premiums for the duration of the calculation.

47. The balance-sheet provision for increasing age for a policyholder is given by the following equation where the provision is revalued annually:

(

)

(

)

(

)

1 1 1+ = + ⋅ − + t i ) t , j ( x ) t , j ( x ) t , j ( x t j t j P K RZ q w V V where t j

V provision for increasing age for policyholder j in year t (without shock),

t j

P net premium for policyholder j in year t, RZ actuarial interest rate,

x(j,t) age of policyholder j in year t, Kx actuarial per capita claim for age x, qx actuarial mortality rate for age x, and

wx actuarial lapse probability for age x. 48. At the end of year t, actuarial funds of

(

1

)

+1 ⋅ − − t j ) t , j ( x ) t , j ( x w V q

are available for every policyholder j for forming the future provision.

However, in the event of deviation from mortality by a factor (1 + a), funds amounting to

(

(

)

)

1 1 1 + ⋅ − + ⋅ − t j ) t , j ( x ) t , j ( x a w V q

are needed.Thus, this change in mortality has the following effect on the result at the end of year t:

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(

(

)

(

(

)

)

)

1 1 1 1 1 + + ⋅ ⋅ = ⋅ − + ⋅ − − − − t j ) t , j ( x t j ) t , j ( x ) t , j ( x ) t , j ( x ) t , j ( x w q a w V a q V q .

49. For the sake of simplicity it can be assumed that the change in mortality in the shock scenario relates to actuarial mortality. However, if the data is available, the actual mortality figure can be used instead. For the resulting weighted mortality q for the whole portfolio, for all 0 ≤ t < Nqxdown , the equation ∑ + ∑ + ⋅ ≈ ⋅ j t j j t j ) t , i ( x V q V q 1 1

should approximately hold good.

50. For the shock, where a = –20%, the best-estimate underwriting surplus for t < Nqxdown is replaced by t t vtÜ t vtÜ t i V q % relZ P Z + ⋅ ⋅ − ⋅ = + 1 20 1 where

it interest rate to term t resulting from the risk-free interest rate term structure

t

V provision for increasing age for portion of the portfolio under consideration at time t

51. Additional income resulting from a longer stay in the pool is disregarded for the sake of simplicity.

52. The capital charges SLT longevity

Health and SLT

longevity

nHealth can then be derived directly from ∑i (∆NAV|longevity) and ∑i (∆nNAV|longevity).

3.2 Mortality risk

53. The mortality shock assumes a permanent 15% increase in mortality, where an increase in the mortality rate leads to an increase in the value of the technical provisions.

54. The technical specifications for QIS 5 (see SCR.8.19.) require that the risk of loss of future income through the early death of policyholders is

considered for inflation-neutral valuation. As the underwriting surplus ZtvtÜ in subsection 26. is calculated on the basis of future premiums, the effect of the shock can be calculated through the fall in premiums.

55. It is also needs to be borne in mind that, until premiums are adjusted to the higher mortality rates, the surplus will change due to additional inheritance, which are taken into account by modifying ZtvtÜ.

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56. The capital charges SLT mortality

Health and SLT

mortality

nHealth can then be derived directly from ∑i (∆NAV|mortality) and ∑i (∆nNAV|mortality).

57. If (1 – qt – wt) represents the average annual probability of staying in the pool in year t before the shock, then the average portfolio size for t = 0 to ω changes by the factor

(

)

(

)

∏ = − − − ⋅ − = t ' t ' t ' t ' t ' t mortality t w q w q % f 0 1 115 1 , where

qt denotes the average probability of mortality in year t and

wt denotes the average lapse probability in year t. 58. The values for qt and wt are to be ascertained on an undertaking-specific

basis for t = 0. The subsequent values are determined in one-year steps on the basis of current probability tables and average annual portfolio ageing of 1 year.

59. Nqxup denotes the period until premiums are adjusted in line with the increased mortality rate.

Loss resulting from reduction of premiums

60. For the period until premium adjustment (t < Nqxup), where Pt denotes premiums as per cash flow

we obtain the new premium resulting from the mortality shock from

mortality t P mortality t t P f ⋅ = ,

by multiplying the change in the portfolio by the old premium.

61. From Nqxup the premium adjustment resulting from the changed mortality rate must also be taken into account. The new premium is set such that the equation

(

)

(

)

(

)

∑ ω = − ω = + − − + ⋅ ⋅ = + ⋅ qxup qxup qxup qxup qxup qxup qxup t N N t mortality t N mortality t N N N t t N t mortality t RZ P V f i RZ L f 1 1 1 , where

Lt denotes payouts as per cash flow, and

qx N

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holds good.

62. Therefore, for t ≥ Nqxup

(

)

(

)

(

)

t N s s N s N mortality s N N N s s N mortality s mortality s mortality t P RZ P V f i RZ L f P qxup qxup qxup qxup qxup qxup qxup ⋅ + ⋅ ⋅ + − + ⋅ = ∑ ∑ ω = − ω = − 1 1 1 is set as an approximation.

63. The annual loss from the mortality shock amounting to

(

)

vtÜ

t mortality

t P relZ

P − ⋅

is calculated by replacing Pt in the calculation of ZtvtÜ in subsection 26. with

mortality t

P .

Change of surplus resulting from additional inheritance

64. In the first Nqxup years until premiums are adjusted in line with the increased mortality rate, additional surpluses arise (analogously to subsections 47. to 50., but with a = +15%), amounting to

t t mortality t i V f q % + ⋅ ⋅ ⋅ + 1 15 1 ,

which, in addition to the operation in subsection 63, can be applied directly to increase Ztvt.

3.3 Lapse risk

65. For QIS 5, the lapse risk for SLT health insurance is ascertained for both an increase and a decrease in the lapse rates. The capital charges SLT

lapse

Health

and SLT

lapse

nHealth are derived from

max

{

∑i

(

∆NAV|Lapseup

)

;∑i

(

∆NAV|Lapsedown

) (

;∑i ∆NAV|Lapsemass

)

}

and

max

{

∑i

(

∆nNAV|Lapseup

)

;∑i

(

∆nNAV|Lapsedown

) (

;∑i ∆nNAV|Lapsemass

)

}

3.3.1 Decrease in lapse rates

66. A permanent 20% decrease in lapses is assumed for the shock for all policies that are adversely affected by such risk.

(17)

67. For the inflation-neutral valuation, the impact of the shock on the future surplus is calculated for the period up to adjustment to the decrease in lapse rates Nwxdown.

68. It is to be assumed for the sake of simplicity that the change in the lapse rates in the shock scenario relates to the actuarial lapse rates. However, if the data is available, the actual lapse rates can be used instead. For the resulting weighted lapse probability w for the whole portfolio, for all 0 ≤ t < Nwxdown, the equation

+ ∑ + j t j j t j ) t , i ( x V w V w 1 1

should approximately hold good.

69. Analogously to subsections 47. to 50., for the decrease in lapse rates the best-estimate underwriting surplus is replaced in the inflation-neutral valuation by t t vtÜ t vtÜ t i V w % relZ P Z + ⋅ ⋅ − ⋅ = + 1 20 1 for t < Nwxdown.

70. Additional income resulting from a longer stay in the pool is disregarded for the sake of simplicity.

3.3.2 Increase in lapse rates

71. A permanent 20% increase in lapses is assumed for the shock for all policies that are adversely affected by such risk.

72. If (1 – qt – wt) represents the average annual probability of staying in the pool in year t before the shock, then the average portfolio size for t = 0 to ω changes by the factor

(

)

(

)

∏ = − − ⋅ − − = t ' t ' t ' t ' t ' t lapseup t w q w % q f 0 1 120 1 ,

where the probability of mortality qt and the lapse probability wt are ascertained as in subsection 58.

73. Below Nwxup denotes the period until premiums are adjusted in line with the increased lapses.

Loss resulting from reduction of premiums

74. As with the mortality shock, we obtain the new premium resulting from the increase in the lapse rates

t lapseup t lapseup t f P P = ⋅ , for t < Nwxup

(18)

and

(

)

(

)

(

)

t N s s N s N lapseup s N N N s s N lapseup s lapseup s lapseup t P RZ P V f i RZ L f P wxup wxup wxup wxup wxup wxup wxup ⋅ + ⋅ ⋅ + − + ⋅ = ∑ ∑ ω = − ω = − 1 1 1 , otherwise

75. The annual loss from the increase in lapse rates amounting to

(

)

vtÜ

t lapseup

t P relZ

P − ⋅

is calculated by replacing Pt in the calculation of ZtvtÜ in subsection 26. with

lapseup t

P .

Change of surplus resulting from additional inheritance

76. In the first Nqxup years until premiums are adjusted in line with the

increased lapse rate, surpluses arise (analogously to subsections 47. to 50., but with a = +20%), amounting to

t t lapseup t i V f w % + ⋅ ⋅ ⋅ + 1 20 1 ,

which, in addition to the operation in subsection 75., can be applied directly to increase Ztvt.

3.3.3 Mass lapse event

77. The shock assumes that for one time 30% of the policies will be cancelled that are affected adversely by such risk.

78. The average portfolio size changes by the constant factor

(

)

(

0 0

)

0 1 30 1 w q % q flapsemass − − − − = ,

where the probability of mortality q0 and the lapse probability w0 are ascertained as in subsection 58.

Loss resulting from reduction of premiums

79. As the shock occurs only for one year, in contrast to the mortality shock and the increase in lapse rates no premium adjustment is necessary. So the new premiums result from

t lapsemass t lapsemass t f P P = ⋅ .

(19)

80. The annual loss from the increase in lapse rates amounting to

(

)

vtÜ t lapsemass t P relZ P − ⋅

is calculated by replacing Pt in the calculation of ZtvtÜ in subsection 26. with

lapsemass t

P .

Change of surplus resulting from additional inheritance

81. In the first year surplus arise (analogously to subsections 76) amounting to

(

)

t t i V w % + ⋅ − + 1 30 1 0 ,

which, in addition to the operation in subsection 80., can be applied directly to increase Ztvt.

3.4 Disability/morbidity risk

82. For QIS 5 a distinction is drawn between income protection insurance and other types of health insurance. The capital charges SLT

morbidity / y disabbilit Health and SLT morbidity / y disabbilit

nHealth are derived from the sum of

∑i (∆NAV|other health insurance) + ∑i (∆NAV|income insurance) and

∑i (∆nNAV|other health insurance) + ∑i (∆nNAV|income insurance). 83. In addition, a distinction needs to be drawn between the shocks resulting

from an increase and a decrease in benefits for other health insurance. If Sup and Sdown denote these shock scenarios, then we obtain

∑i (∆nNAV|S) = max{∑i (∆nNAV| Sup);∑i (∆nNAV| Sdown) and ∑i (∆NAV|S) =

(

)

(

)

(

)

(

)

(

)

(

)

(

) (

)

{

}

     ∆ ∆ ∆ < ∆ ∆ ∆ > ∆ ∆ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ otherwise. , if , if , i down i up i i down i up down i i down i up up S | NAV ; S | NAV max S | nNAV S | nNAV S | NAV S | nNAV S | nNAV S | NAV

84. The period up until premiums can be adjusted to neutralise the effects of the shock is denoted by NVL.

3.4.1 Increase in income insurance benefit

85. The shock assumes a 50% increase in payouts for income insurance in the first year and an increase of 25% in all subsequent years.

(20)

86. This means that, using the benefit payments Lt defined in the cashflow, the best-estimate underwriting surplus for the time points t < NVL is replaced by    = ⋅ ⋅ φ − ⋅ = sonst , 25 0 t falls , 50 % % L SQ relZ P Z vtÜ t t vtÜ t where SQ

φ indicates the average ratio of the paid and the calculated insurance benefits for income insurance for the last five years.

If no separate data is available for income insurance benefit, then the data is to be estimated by an appropriate method. If data for five years is not available, then we set

φSQ = 1.

The first three years after establishment of the undertaking can be disregarded.

3.4.2 Increase in other health insurance benefits

87. The shock for other health insurance assumes a one-off 5% increase in insurance benefits and a 1 percentage point rise in annual medical inflation. 88. This means that, using the benefit payments Lt defined in the cash flow,

the best-estimate underwriting surplus for the time points t < NVL is replaced by + ⋅ = vtÜ t vtÜ t P relZ Z φSQ — Lt — (1 – (1 + 1%)t — (1 + 5%)) where SQ

φ indicates the average ratio of the paid and the calculated insurance benefits for other health insurance for the last five years.

If no separate data is available for other health insurance, then the data is to be estimated by an appropriate method. If data for five years is not available, then we set

φSQ = 1.

The first three years after establishment of the undertaking can be disregarded.

(21)

3.4.3 Reduction in insurance benefits for other health insurance

89. The shock for other health insurance assumes a one-off 5% reduction in insurance benefits and a 1 percentage point fall in annual medical inflation. 90. The benefit payments after the shock until premiums are adjusted after NVL

years are, for t = 0 to ω

L L

(

)

min{t;NVL}

(

%

)

t down

t = ⋅ 1−1% ⋅ 1−5 ,

where

Lt denotes benefit payments as per the cash flow for other health insurance

down t

L denotes benefit payments for other health insurance after the reduction in insurance benefits until NVL.

Income resulting from reduction in insurance benefits

91. In the first NVL years until premiums are adjusted to the lower claims level, additional surpluses arise amounting to

(

down

)

t t L L SQ⋅ − φ ,

which can be applied directly to increase Ztvt; the calculation of φSQ is set out in subsection 88.

Loss resulting from reduction in insurance benefits

92. The new premium at time NVL is set such that the equation

(

)

(

)

(

)

∑ ω = − ω = − + = ⋅ + − + VL VL VL VL VL VL VL t N t N down t N N N N t t N down t RZ P V i RZ L 1 1 1 , where down t

P denotes the new premium for other health insurance resulting from the reduction in insurance benefits holds true.

93. To take account of the reduction in insurance benefits the underwriting surplus ZtvtÜ in subsection 26 for t ≥ NVL is therefore modified by the factor

(

)

(

)

(

)

(

)

(

)

∑ ∑ ∑ ∑ ω = − ω = − ω = − ω = − + ⋅ + − + = + + VL VL VL VL VL VL VL VL VL VL VL N t t N t N N N N t t N down t N t t N t N t t N down t RZ P V i RZ L RZ P RZ P 1 1 1 1 1

(22)

3.5 Expense risk

94. The shock assumes a one-off 10% increase in expenses and a 1 percentage point increase in annual medical inflation.

95. The period until premiums can be adjusted to neutralize the effects of the expense shock is denoted by NKosten.

96. For the expense shock this means that the best-estimate underwriting surplus t < NKosten is replaced by

(

vtÜ rel

(

)

t

(

)

rel

)

t vtÜ

t P relZ Kosten % % Kosten

Z = ⋅ +φ − 1+1 +1⋅ 1+10 ⋅φ where ∑ ∑ − − = − − = = φ 6 2 6 2 s s s s rel P Kosten Kosten and

Kostens = denotes acquisition and administration expenses and expenses for settling insurance claims

= statement 234 page 1 column 2 line 20 + statement 235 page 1 column 2 line 10 + statement 235 page 1 column 2 line 21. 97. The term rel

Kosten

φ may also be limited to a market value. If the figure calculated for Kostenrel

φ does not appear representative for the future or cannot be calculated owing to lack of data, then the future ratio of expenses to premiums should be estimated by an appropriate method. In this instance, it is sufficient to enter an absolute level of expenditure for Kosten-2 in the calculation guide.

(23)

4 Model parameters Variable Definition in subsection Value N 10. NZins or ω+1 k 11. NZins NZins 15 5 iMarge 21. 0.1% M 26. 5 Nqxup 59. 2 Nqxdown 46. 3 Nwxup 73. 3 Nwxdown 67. 3 NVL 84. 2 NKosten 95. 3

References

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