MANAGING LONGEVITY RISKS IN THE FINANCIAL MARKETS: INNOVATE OR DIE

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1 UNIVERSITÉ PARIS-DAUPHINE Chaire: «Les Pariculiers face au Risque» Séminaire Ageing and Risk MANAGING LONGEVITY RISKS IN THE FINANCIAL MARKETS: INNOVATE OR DIE JORGE MIGUEL BRAVO Universiy of Évora, Deparmen of Economics Évora Porugal, Paris, December 2, 2008 Jorge Miguel Bravo (2008) 1

2 Agenda 1. Longeviy: macro effecs 2. The naure of moraliy and longeviy risks 3. Projecing moraliy rends 4. Hedging individual longeviy risk annuiies, reverse morgages 5. Hedging corporae longeviy risk Porfolio diversificaion Produc redesign, buyou of he liabiliies Reinsurance markes Securiizaion: Longeviy/survivor bonds Moraliy-linked derivaives Jorge Miguel Bravo (2008) 2

3 Longeviy: macro effecs Reforms in social securiy sysems Increase in conribuion raes Reducion in pension/salary raios Increase in reiremen age Defined Benefi Defined Conribuion Mobiliy of he workforce, Labour marke uncerainy, Increasing pressure on public finances Changes in he consumpion/saving srucure Increase in he capial/labour raio real ineres raes decline Asse meldown Reducion in he reiremen income ha is guaraneed Individuals will have o become more self-relian Jorge Miguel Bravo (2008) 3

4 Moraliy risk and Longeviy risk Projeced (solid line) vs experienced (dos) moraliy raes for a given age x q () x q () x q () x q () x q () x q () x ( A) ime ( B) ime ( C) ime Case (A): random flucuaions around expeced values Case (B): random flucuaions around and random deviaions from expeced values Case (C): random flucuaions and caasrophe moraliy Jorge Miguel Bravo (2008) 4

5 Moraliy risk and Longeviy risk Case (A) Process risk Pooling risk (large, homogeneous porfolios) Hedging hrough enforcemen of pooling effecs Case (C) Sysemaic risk (bu higher moraliy han expeced) Case (B) Experienced rend differen from expeced one sysemaic risk, radiional hedging ools do no apply Longeviy risk: he risk ha individuals will sysemaically live longer han expeced Moraliy risk: he risk ha individuals will live shorer han expeced (i.e., heir moraliy is higher han expeced) Jorge Miguel Bravo (2008) 5

6 Moraliy risk and Longeviy risk Moraliy rends require he adopion of projeced lifeables when living benefis are deal wih Whaever projecion model is adoped, he fuure moraliy is random sysemaic deviaions may occur Deviaions from expeced values are explained by he sochasic naure of moraliy process risk he calculaion of expeced moraliy raes is based on he choice of a projecion model model risk he esimaion of he parameers of he projecion model parameer risk A useful framework is given by sochasic moraliy models Jorge Miguel Bravo (2008) 6

7 Projecing moraliy rends Approaches in consrucing prospecive lifeables Verical Horizonal Diagonal Projecion Mehods Parameric models Mehods based on moraliy profiles Lee-Carer mehodology Poisson log-bilinear mehodology Projecion wih reference o limi lifeables Projecion wih reference o opimal and/or model lifeables Age-period-cohor models, Jorge Miguel Bravo (2008) 7

8 Hedging individual longeviy risk Imporance of financial inermediaries/markes 1. In he accumulaion phase (acive life) Flexibiliy (amoun and iming of heir conribuions) Efficiency (invesmen diversificaion, gradual adjusmen of he risk/reurn profile based on age, ax advanages, ) 2. In he decumulaion phase (reiremen) Smooh access o he accumulaed wealh Proecion agains longeviy/inflaion various ypes of annuiies healh care and long-erm care insurance wealh moneisaion (e.g., reverse morgages) Jorge Miguel Bravo (2008) 8

9 Annuiy markes consrains Demand consrains Annuiies are perceived as expensive Seen only as a financial invesmen in he accumulaion phase Insufficien ax incenives Beques, liquidiy and inflaion moives «crowding-ou» effec induced by generous public pensions Supply consrains Adverse selecion problems Pricing problems: lack of prospecive lifeables Lack of soluions o manage longeviy, ineres rae and inflaion risks Regulaion Jorge Miguel Bravo (2008) 9

10 Reverse morgages: definiion Financial produc ha allows individuals (reirees) o conver heir real sae wealh ino eiher a lump sum or a annuiy income and, a he same ime, o remain in heir homes unil hey die, sell or vacae heir homes o live elsewhere Comparison wih convenional loans There are no repaymens made during he course of he loan Loans accrue wih ineres and possibly adminisraive fees and are seled only upon he deah of he borrower, sale of he propery or he vacaion of is residens No asses oher han he home may be aached o deb repaymen ( non-recourse loan) Loans are underwrien on he sole basis of he propery value Jorge Miguel Bravo (2008) 10

11 Reverse morgages: risks Risks o he lender/loan provider Crossover risk: loan value exceeds he collaeral house value Longeviy risk / Occupancy risk Ineres rae risk House price risk Oher risks: mainenance risk, expenses risk Pricing lump sum reverse morgages Q 0 =loan value; H 0 = house value; M =cos of capial Value of a reverse morgage loan V min( Q, H ) Jorge Miguel Bravo (2008) 11

12 Reverse morgages: pricing Loss o he lender: L M V M min( Q, H ) Loan amoun accumulaes a risk-free ineres rae plus a risk premium, he house price appreciaes a a rae of and he cos of capial accumulaes a a rae of Value of he loan repaymen 0 Q Q exp ( r ) ds 0 H H exp ds M Q exp ds s s s 0 0 V min( Q exp ( r ) ds, H exp ds ) 0 s 0 s Jorge Miguel Bravo (2008) 12

13 Reverse morgages: pricing Loss o he lender, admiing ha he life span of he reverse morgage loan is a random variable T T T T L Q exp ds min( Q exp ( r ) ds, H exp ds ) T 0 s 0 s 0 s Acuarial equivalence principle rt Ee ( L T ) 0 Pricing equaion for a reverse morgage T T T 0 s 0 s 0 s E Q0exp ds E min( Q0exp ( r ) ds, H0exp ds ) Jorge Miguel Bravo (2008) 13

14 Hedging company longeviy risk Approaches in managing longeviy risk 1. Hedge he risk while reaining i Porfolio diversificaion 2. Reduce he risk by ransferring i o anoher counerpar Produc redesign Buyou of he liabiliies Reinsurance reaies (surplus, XL, Sop-Loss, ) Securiizaion: Longeviy/survivor bonds Moraliy-linked derivaives: forwards/fuures, swaps, opions, longeviy caples/floorles, swapions, Jorge Miguel Bravo (2008) 14

15 Hedging longeviy risk: diversificaion Explore naural hedging opporuniies combining porfolios wih complimenary cash flows Long vs shor exposure Annuiies, DB pension plans shor longeviy or, equivalenly, long moraliy Life insurance porfolio long longeviy or, equivalenly, shor moraliy Inernaional diversificaion moraliy shifs observed in differen counries are no perfecly correlaed Moraliy shifs affec differen socioeconomic groups differenly Diversificaion enhancemen hrough swap agreemens Jorge Miguel Bravo (2008) 15

16 Risk ransfer mechanisms: produc redesign Increase safey loadings Annuiies wih premiums indexed o he evoluion of longeviy Replace radiional non-paricipaing annuiies wih paricipaing (wih-profi) conracs ha pass par of he exposure o longeviy risk o surviving paricipaing policyholders should offer addiional reurn o compensae for longeviy risk Pricing sraegies ha differeniae among individuals according o heir specific risk facors (e.g., smoking) coningency loadings Alernaive: Buyou (exernalizaion) of he pension plan Jorge Miguel Bravo (2008) 16

17 Capial marke soluions: Longeviy Bonds General srucure Bond whose coupons and/or principal are linked o he evoluion of a survivor index in a given reference populaion Types of Longeviy Bonds (LBs) Longeviy Zeros (LZs): similar o zero coupon bonds Survivor bonds: coninue o make paymens for as long as any member of he populaion is sill alive Principal-a-risk LBs: fixed or ineres rae sensiive coupons, bu whose principal is coningen upon he evoluion of a survivor index Inverse LBs: comparable wih convenional floaers Deferred longeviy bonds Moraliy Caasrophe Bond Jorge Miguel Bravo (2008) 17

18 Longeviy bonds: complicaions (1) Imbalance in he marke: naural excess of demand Poenial issuers: privae companies wih a naural long exposure o longeviy risk (e.g., pharmaceuicals, residenial car homes, housing associaions, bioech companies) Governmen issuance of LBs (pros and cons) In order o suppress a marke failure (lender of las resor) By spreading he risk over a huge amoun of axpayers his will eliminae he marke price of risk Saes conribue o he increase in longeviy allows a more efficien inergeneraional risk sharing The sae is already highly exposed o longeviy risk hrough DB pension sysems The sae diversifies only wihin he axpayers group Jorge Miguel Bravo (2008) 18

19 Longeviy bonds: complicaions (2) Survivor Index problems Indexes are consruced from daa published infrequenly and subjec o incurred-bu-no-repored errors The hisorical daa ypically needs o smoohed mehod risk Indexes are subjec o inegriy and conaminaion risk Issues of moral hazard: daa providers have much earlier access o daa han invesors Survivor indexes involve projecions of fuure moraliy ha are subjec o boh model and parameer risk Jorge Miguel Bravo (2008) 19

20 Longeviy bonds: complicaions (3) Valuaion We canno use sandard non arbirage argumens o price longeviy securiies because of marke incompleeness Modelling issues: represenaion of moraliy uncerainy Esimaion issues: in paricular, marke price of longeviy risk Esimaing he marke price of longeviy risk Risk-neural approach Use classic premium principles (e.g., sandard deviaion principle) Disorion approaches (Wang ransform) Sharpe raio Consumpion CAPM Mean-variance and Risk minimizaion sraegies Jorge Miguel Bravo (2008) 20

21 Moraliy-derivaives Moraliy Swaps Example: vanilla moraliy swap Analogous o an ineres rae swap (IRS) Agreemen beween wo counerparies o exchange prese paymens ha decline over ime in line wih he survivor index anicipaed a ime 0 (fixed leg), for paymens dependen on he realised value of he survivor index a ime (floaing leg) Moraliy Fuures Underlying asse (process): Longeviy Bonds, annuiies, survivor index Delivery daes Criical issues: need for a large, acive, liquid spo marke for he underlying Jorge Miguel Bravo (2008) 21

22 Moraliy-derivaives Moraliy Opions Useful for a hedger who wans o proec heir downward exposure, bu leave upside poenial Speculaors who wish o rade views on he volailiy of moraliy raes raher han on he levels The valuaion and risk managemen of opions requires a good sochasic moraliy model, e.g., affine-jump diffusion model d () a () d () dw() dj(), () 0 x x x x x Possible ypes of opions Survivor caps and floors Annuiy fuures opions Moraliy swapions Jorge Miguel Bravo (2008) 22

23 MERCI DE VOTRE ATTENTION ET UN BON NÖEL JORGE MIGUEL BRAVO Universiy of Évora, Deparmen of Economics Évora Porugal, Jorge Miguel Bravo (2008) 23

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