Stress test for measuring insurance risks in non-life insurance

Transcription

1 PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance rsks and expense rsk for nonlfe nsurance n the traffc lght model. Background and purpose Fnansnspektonen s (FI) ntenton wth the new expanson of the traffc-lght model for non-lfe nsurance s to stress tems n the company s balance sheet ncludng both the asset and the lablty. The sze of the changes wll be chosen such that t approxmately represents the 99.5 percent quantle of possble devatons n one year. Ths document descrbes how assumptons for nsurance rsks for non-lfe nsurance are chosen. Changed assumptons for non-lfe nsurance The changed assumptons for the provsons n non-lfe nsurance companes nclude A best estmate n accordance wth the Prudent Person Prncple Captal requrements for ncrease of provsons for unearned premums and unexpred rsks Captal requrements for ncrease of provsons for outstandng clams Captal requrements for catastrophe rsk Captal requrements for expense rsk Best estmate n accordance wth the Prudent Person Prncple A best estmate accordng to the Prudent Person Prncple shall correspond to the expected value of the amounts whch the company needs to fulfll the commtments whch can reasonably be expected. Dscountng of the future payments shall be done wth a rsk-free nterest rate. The calculatons shall be made wth approprate actuaral methods and refer to busness gross of rensurance. Box 781 SE Stockholm, Sweden [Brunnsgatan 3] Tel Fax [email protected] Captal requrements for ncreased provsons for unearned premums and unexpred rsks KPR The rsk factors for these provsons are of two types: Parameter rsk and Volatlty rsk. 1(6)

2 Parameter rsk The Parameter rsk les prmarly wthn clam nflaton and clam frequency. The average duraton of the remanng perod of rsk s often about sx months. The ncrease n clam frequency s assumed to be 10% per year and the ncrease n nflaton % per year, both above those that have been used n the best estmates. The total ncrease n the company s provsons for unearned premums and unexpred rsks because of uncertanty n parameters s therefore (10% + %) 6/1 = 6% of the company s provsons for unearned premums and unexpred rsks (AEIPKR),.e. KPRPAR 6 % Volatlty rsk AEIPKR The volatlty rsk descrbes uncertanty about the outcome of the nsurance busness durng the perod whch unearned premums are supposed to cover. The captal requrement for branch number s determned from the numbers n = expected number of clams, nl-clams excluded, durng the followng 1- month-perod for branch number, net rensurance m = expected clam sze, nl-clams excluded, for branch, net rensurance v = coeffcent of varaton n the clams dstrbuton, nl-clams excluded, for branch number, net rensurance The captal requrement s determned by the formula KPRSLUMP n,58 m 1 v The total captal requrement for volatlty rsk s determned by a square root summaton over branches by KPRSLUMP KPRSLUMP The captal requrement for unearned premums and unexpred rsks s KPR KPRPAR KPRSLUMP Captal requrement for ncreased provsons for outstandng clams KOS The rsk factors for these provsons are prmarly clam amounts, clam nflaton and payment patterns. FI has estmated the uncertanty n made provsons by studyng the varaton n the supplementary payment factor,.e. the rato be-

3 tween total compensaton and pad compensaton to date. In order to more accurately estmate the standard devatons, the companes have been dvded nto three more homogenous groups: AFA Health and Sckness Natonal companes except AFA Health and Sckness Large local companes. The standard devaton s a measure for uncertanty. Let (.) be a notaton for standard devaton and denote the supplementary payment factor by SPF. Then the followng holds: Total compensaton SPF Pad to date Pr ovsons Total compensaton Pad to date Pad to date ( SPF 1) (Pr ovsons) Pad to date ( SPF) FI has estmated the standard devaton D for the supplementary payment factor for the total payments wthn the company groups by nsurance branch and development year D. The estmatons of the standard devatons for the three groups are gven n the publshed spreadsheets on Fnansnspektonen webste under the folder Reportng/Traffc-lght model" The standard devatons D for the supplementary payment factor shall thus be appled to the clam years t = R D for D = 0, 1, For an ndvdual company B, the standard devaton s Bt for the provsons for branch and clam year t s calculated as D s max1 c ;0,7 (1 c ) mn u ; 0,5 f abt Bt Bt Bt Bt Bt where c Bt = the company s estmated share of rensurance ceded for nsurance branch and year t u Bt = the company s payments to date for nsurance branch and clam year t D = the standard devaton accordng to the table above, where D = R t a Bt = the company s market share n ts group for nsurance branch and clam year t f Bt = the company s provsons for outstandng clams for nsurance branch and clam year t 3

4 The share of ceded rensurance can be estmated by the rato between the premums for ceded rensurance and the total premum or the rato between compensatons from rensurance companes and total compensatons. The market share s measured wth the ad of the premum share n the company group as a Bt p 1 Bt max ; Pt 9 where p Bt = the company s premum for nsurance branch and year t P t = total premum n the company group for nsurance branch and year t The total premums P t for the three groups are gven n the publshed spreadsheets on Fnansnspektonen webste under the folder Reportng/Traffc-lght model" AFA has the share 1 n ts company group. The standard devaton s B(yngre) for the company s provsons for outstandng clams for nsurance branch s calculated by the square root formula: s B s ( yngre) t Bt where the sum s calculated for the more recent clam years for whch the standard devatons are calculated as above. These years do not represent the entre provsons for outstandng clams, rather n terms of experence, there are mnor provsons for clam years older than those reported separately. These older clam years represent the shares b of the total provsons for the three groups are gven n the publshed spreadsheets on Fnansnspektonen webste under the folder Reportng/Traffc-lght model" Table 5. Percentage for older clam years b Under the assumpton that the relatve standard devaton for uncertanty n the provsons for the older clam years s the same as the more recent clam years, s B( äldre) s B( yngre) b 1 b 4

5 The total standard devaton then becomes s B s s B( yngre) B( äldre) The above calculatons can only be completed for those nsurance branches where Fnansnspektonen has access to relable statstcs. For the branches Drect foregn nsurance Rensurance receved from Swedsh companes Rensurance receved from foregn companes the followng standard amounts shall be appled: s B,utl = 0.06 the provsons for outstandng clams s B,mott sv åf = 0.15 the provsons for outstandng clams s B,mott utl åf = 0.0 the provsons for outstandng clams The standard devaton s B for the company s total provsons for outstandng clams s also calculated wth the square root formula s s s s s B B B, utl B, mott sv åf B, mott utl åf Captal requrements for provsons for outstandng clams The captal requrements n the company s provsons for outstandng clams (KOS) s calculated as KOS =,58 s B Captal requrements for catastrophe rsk The company shall estmate the costs net of rensurance from the followng three catastrophes. The costs shall be valued as the best estmate of the effect on the company f the catastrophe occurs where the company s actve. A catastrophe, the effect of whch s less than 5 % of the largest, need not be valued and can be neglected. Catastrophe 1 A storm resultng n a total loss n the Swedsh market of SEK 15 bllon, affectng nsurance class Property (Commercal and property, homeowners). Catastrophe A fnancal crss resultng n a market loss of SEK bllon, affectng nsurance class Credt nsurance. 5

6 Catastrophe 3 An epdemc resultng n a market loss of SEK 1 bllon affectng nsurance class Personal accdent and sckness. The captal requrement s determned as follows: KKAT KAT where KAT, = 1,,3, s the net cost for catastrophe 1 (storm), catastrophe (fnancal crss) and catastrophe 3 (epdemc). Captal requrements for non lfe nsurance rsk KS KS KOS KPR 0,5 KOS KPR KKAT Expense rsk The purpose for testng expense rsk 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 rsk shall be reported separately and shall not be ncluded under the term nsurance rsk. The expense rsk s measured by K = the company s annual fxed costs, defned as operatng expenses plus clams adjustment costs mnus acquston costs. The captal requrement for expense rsk s calculated as 0.1K. Expense rsk and nsurance rsk are assumed to have a correlaton coeffcent of 50 % when calculatng the total rsk. 6