An economic and actuarial analysis of death bonds

Transcription

1 w w w. I C A o r g A ecoomic ad acuarial aalysis of deah bods JOÃO VINÍCIUS DE FRANÇA CARVALHO UNIVERSITY OF SAO PAULO, BRAZIL LUÍS EDUARDO AFONSO UNIVERSITY OF SAO PAULO, BRAZIL

2 Ageda Iroducio Objecives The fiacial produc deah bod Mehodology Simulaios Adverse Selecio: he mos lucraive isured Fial remarks 2

3 Iroducio Life isurace: payme of a ammou o beeficiaries a he ed of he year of deah of he isured; Tradiioally, life isurace has bee reaed as a illiquid asse; I some couries, he policies have bee egoiaed i he secodary marke (deah bod); Pricig problem: cerai receivig bu ucerai eecuio ime; Ivesor s rae of reur depeds o isured s probabiliy of deah. 3

4 Objecives Aalyze he feasibiliy of his marke, hrough simulaios of he primary ad secodary pricig of such securiies; Evaluae possible marke failures. 4

5 The fiacial produc deah bod 5

6 Mehodology The rae of reur depeds o he fiacial amou ha a idividual has maaged o accumulae i he eiy i capializaio fiacial sysem; The premium calculus is se o equalize he amou o be paid wih he epeced prese value (EPV) of paymes i he fuure; EPV depeds o: survival fucio ad ieres rae acuarial modelig. 6

7 Mehodology : fiacial discou facor; l e d : umber of livig people aged ad dead persos before achievig +1 years old, respecively, give oe survival fucio; p : probabiliy of a idividual a age complee age + ( q = 1 - p ). 7

8 8 Pure sigle premium (PSP) :, e Le: D = v l, C = v +1 d ad M =, so: Aiuies: le N =, we ge: Ne level aual premium (NLAP): Accumulaed reserves i years: d v l q v A C D M C D d v l v q v A D D N D D D D p v ä 1 N M ä A P A P ä D P N M ä P A V. Mehodology

9 Paid-up isurace: allows reegoiaio of he value of he beefi, from a reserve already accumulaed. The formula is give by: Profiabiliy of he deah bod: 9 P P A ä P A A V W 1. V V j W K RR ) (1.,, Mehodology

10 Epeced rae of reur (ERR,, ): 1 i i i i p q V V j W K p q ERR 1 1,, ) (1. Mehodology

11 Rae of Reur of he operaio (%) Simulaios Geder (M/F) M Age a hirig (, i years) 35 Number of NLAP paid (, i years) 15 Age a egoiaio ( +, i years) 5 Fiacial discou (per year) 2% Accumulaed Reserve ( V ) R$ 21, Capial (K) R$ 1,. Paid-up isurace (K. W ) R$ 4.352, Age of Deah (years) 11

12 Probabiliy of deah a age Simulaios,4 1,35,9,8,3,7,25,2,15,1,6,5,4,3,2 Accumulaed Probabiliy,5, Age of Deah (years) 12

13 Reur (i %) Simulaios Survival (i years) Se = M; Age of Coracig = ; Age of Negociaio = 2 Se = F; Age of Coracig = ; Age of Negociaio = 2 Se = M; Age of Coracig = 2; Age of Negociaio = 4 Se = F; Age of Coracig = 2; Age of Negociaio = 4 Se = M; Age of Coracig = 4; Age of Negociaio = 6 Se = F; Age of Coracig = 4; Age of Negociaio = 6 Se = M; Age of Coracig = 6; Age of Negociaio = 8 Se = F; Age of Coracig = 6; Age of Negociaio = 8 Se = M; Age of Coracig = 8; Age of Negociaio = 1 Se = F; Age of Coracig = 8; Age of Negociaio = 1

14 Simulaios Age a egociaio M Geder F 2,9% (32,99%),32% (3,46%) 4,9% (27,11%),33% (25,63%) 6,1% (2,21%),35% (2,1%) 8,18% (11,76%),51% (12,4%) 1,381% (4,47%),83% (4,71%) 14

15 Adverse Selecio: he mos lucraive isured Iformaio asymmeries: he ivesor ca icorrely esimae he ERR; Adverse Selecio: (isiuio) has less iformaio ha he age (isured), wih a uilaeral chage of behavior he ivesor would be more ieresed i idividuals he isured wih higher probabiliy of deah; A hypoheical way o selec hese policyholders: fidig hem wih heir diseases already diagosed; Moraliy Proy: medical lieraure (Eurocare projec) for diagosis of cacer. 15

16 Adverse Selecio: he mos lucraive isured Caegory of probabiliy Average poi of caegory Me Wome Toal 8% 9% 2% 5% 4% 6 79% 7% 31% 45% 38% 4 59% 5% 25% 23% 24% 2 39% 3% 1% 12% 11% <2% 1% 32% 14% 23% Toal 1% 1% 1% Average probabiliy of survivig 5 aos 42,2% 52,5% 47,8% Age a egoiaio M 185,57% (12,64%) 96,91% (8,71%) 39,67% (6,18%) 7,% (4,73%) -5,65% (4,17%) Geder F 23,25% (16,35%) 17,39% (11,18%) 44,29% (7,78%) 6,66% (5,75%) -7,77% (4,97%) 16

17 Fial remarks (I) The firs comparisos bewee he mai facors for pricig, geder ad age, evidece ha iiially his is a low aracive ivesme; Regardless of geder, he older is he isured, he higher is he rae, as also here is higher ieres i wome's lives ha i me s; 17

18 Fial remarks (II) Icreasig probabiliy of premaure deah: high araciveess of he produc by he ivesors (evidece of srog adverse selecio); For fuure sudies, i is possible o hik of he aalysis for oher ypes of diseases or i he more refied modelig of he curve of probabiliy of deah, as well as oher possibiliies of adverse selecio. 18