MATURITY GUARANTEES EMBEDDED IN UNIT-LINKED CONTRACTS VALUATION & RISK MANAGEMENT *

Transcription

1 ABSRAC MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN * Floren PERNOUD hierry FAVRE-BONVIN A key feaure of mauriy guaranees aached o uni-linked life insurance conracs is he uncerainy surrounding he benefi. Wih hese producs an insurance company is direcly exposed o he financial marke and o he need o explain o regulaors, raing agencies and shareholders how hey measure and plan o conrol his risk. One approach by direc insurance companies o hese problems was o rerocede he risk o a reinsurer. Hence he risk is ransferred and wih i many quesions regarding valuaion and risk managemen. Bu he sharp and prolonged fall of global capial markes have occasioned many reinsurers o exi he marke and moreover pushed insurance companies o reassess how hey measure and manage he risk associaed wih mauriy guaranees aached o unilinked life insurance conracs. Here we presen a mehod o evaluae and conrol he risk of such producs under a risk neural world and examine some pracical issues concerning he hedging of such producs. KEYWORDS Garanie Plancher, GMAB, GMDB, Fair Value, Mark-o-Marke, Asse Liabiliy Managemen, Dynamic Hedging, Capial & Reserves requiremens. 1. INRODUCION Mos radiional acuarial Life producs have deerminisic benefis, whereas some conracs in addiion include profis or bonuses allocaed o he policy from he surplus earned by he insurance company. A new ype of life insurance producs links he payoff of he insurance benefis o various asses and no he general accoun. hese asses could be a cerain sock, a baske of socks or simply shares of a muual fund. he laer ype of producs is he opic of his aricle, and we refer o hese conracs as Uni-Linked (UL) producs hough oher names are used depending on he counry: Variable Annuiies in he US, Segregaed Funds in Canada, Uniés de Compe in France. * Paper presened o he 003 Insurance, Mahemaics & Economics Congress floren.pernoud@wanadoo.fr favrebonvin@yahoo.com BULLEIN FRANÇAIS D ACUARIA, Vol. 6, N 11, juin-décembre 003, pp

2 168 F. PERNOUD & h. FAVRE-BONVIN Such producs seem o offer he insurance companies as well as he insurance cusomers advanages compared o radiional producs. Cusomers may benefi from higher yields in financial markes and hen again, he insurance indusry may benefi from offering more compeiive and flexible savings producs. However insurers are facing new and unfamiliar risks oday as hey race o design and disribue innovaive UL producs ha include minimum benefis feaures. No only compeiion bu also cerain regulaors have imposed new sandards in he UL indusry. A Guaraneed Minimum Deah Benefi (Garanie Plancher en cas de Décès) is now embedded in all recen UL conracs sold in Europe or Norh America. More recenly living benefis (Garanie Plancher en cas de Vie) have appeared for he purpose of proecing policyholders wealh agains poor capial markes performance if he insured survives a cerain period. Wha is foreseen as he common life insurance produc in he near fuure, is he UL endowmen insurance, which is a combinaion of a pure endowmen policy (minimum mauriy benefi) and a erm insurance policy (minimum deah benefi) linked o a muual fund. Insurers now confron subsanial exposure o capial marke risks. Capial marke risk in a UL arises from wo main sources. Firs, he revenue of he produc is achieved by charging a guaranee fee, assessed as a percenage charge agains he marke value of he conrac (which is linked by definiion o he underlying asse performance). herefore, if he asse moves down, he insurer collecs a fee applied o a reduced value. he nominal amoun colleced herefore flucuaes in relaion o he capial markes levels. Incidenally, his source of risk concerns he whole savings insurance indusry regardless of any minimum benefi embedded in he conracs. he second main source of marke risk obviously originaes from policy minimum benefis coningen o eiher deah or survival. A policyholder deah or a he mauriy dae if he survived, if he marke value of his invesmen is less han he guaraneed value, he insurer commis o making up he difference. Obviously he higher he guaraneed amoun, he larger he risk for he insurance company. ogeher, as he marke declines an insurer has exposure o increasing claims in addiion o reduced revenues. Applied o he worldwide UL marke size and aking ino accoun he recen crash of inernaional equiy markes, valuaion and risk managemen of such embedded guaranees is a fundamenal challenge o he acuarial profession. Unforunaely, he acuarial world and local regulaors seem o have rereaed ino a srange silence. For he ime being he mos deailed and documened official acuarial guideline comes from he Canadian

3 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN 169 Insiue of Acuaries (CIA) which has devoed an indusry-wide ask force o guaranees associaed o Canadian Segregaed Funds. One poin of his excellen work is ha i has raised he awareness of he unique and significan risks associaed o such guaranees. On a mehodological poin of view he CIA s recommendaion for valuaion and reserving basically consiss in: 1) esimaing he probabiliy disribuion funcion of he presen value of revenues and claims under a hisorical marke reurn model ) seing reserves as a percenile of his disribuion. From our prospecive his mehodology has wo major drawbacks. Firs, he resuls rely heavily on he marke reurn model and is parameers and i hus gives rise o non robus and heerogeneous risk measures among he insurance indusry. he second one is linked o Risk Managemen: indeed his mehod assumes a poor Asse Liabiliy Managemen sraegy ha consiss in running he risk naked and invesing revenues and reserves a he risk free rae. o ha exen he CIA menions ha, if he insurer has anoher ALM sraegy, i could be included in he projecions of fuures cash flows: we are back o square one! Anoher poin is also miigaing he proposal of he CIA: he Inernaional Accouning Sandards (IAS) and he Financial Accouning Sandards from US GAAP saes he concep of Fair Valuaion of risks. According o hese accouning rules he value a financial marke risk has o be he same whoever is carrying i. Such benefis could be easily analyzed as derivaive producs coningen o acuarial facors. herefore we claim ha he valuaion of such financial risk embedded in an insurance conrac has o be consisen wih no-arbirage condiions in he financial markes. In his aricle we rea he case of a pure endowmen benefi i.e Guaraneed Minimum Accumulaion Benefi (GMAB) i.e a mauriy guaranee on a single premium UL conrac. We resric our aenion o his produc because i embeds a high degree of financial risk compared o erm insurance i.e deah benefi his produc and also because i is a ruly innovaive produc for he savings insurance indusry. he major goal of his aricle is o provide insurance praciioners wih a comprehensive valuaion mehodology and a risk managemen sraegy o manage mauriy guaranees embedded in a simple uni-linked conrac. he aricle is srucured ino wo pars. he firs one focuses on he valuaion model using sochasic ineres raes and provides wih numerical examples. he second par describes he oucomes of dynamic hedging and proposes a consisen approach for reserves and capial concerns.

4 170 F. PERNOUD & h. FAVRE-BONVIN. GMAB VALUAION he following sudy focuses on mauriy guaranees or guaraneed minimum accumulaion benefi» (US marke denominaion), ha are added o classical Uni-linked policies. Boyle and Hardy (1997) examine differen ypes of echniques o evaluae hose guaranees. For us hough a Uni-linked insurance conrac wih guaranee has a payoff ha can effecively be represened by simple financial opions, herefore opion pricing heory will be applied for valuaion purposes..1 Conrac descripion We consider a single premium UL conrac wih: a single underlying financial vehicle a mauriy a guaraneed minimum surrender value a mauriy..1.1 Srucure of he benefi A incepion a single premium, S 0, is invesed in a muual fund. During he lifeime of he conrac he value of he invesmen evolves according o he marke value of he muual fund. If he policyholder wihdraws his money before mauriy or in case of deah, he or his beneficiaries will ge he marke value of his conrac from which a surrender charge is deduced. However in case of survival a he mauriy dae he benefis from he guaraneed surrender value i.e he will ge he higher beween he marke value of he conrac and he guaraneed amoun. Le us define S he marke value of he invesmen in he muual fund a ime. In general he minimum guaraneed amoun, denoed K, is a deerminisic funcion of he iniial invesmen, bu i can also be a pah-dependen value of x%max S i 1 marke value (for insance { } i...n = ). he benefi of he conrac can be wrien as follow: + ( S + ( K S ) ) 1[ > ] 1 L [ A > ] ( 1 ς) S 1[ < ] S A L 1[ < ] A L wih L represening he dae when he policyholder leaves he conrac, ς he surrender charge and A represening he dae of deah of he policyholder. As he insurance company holds in is balance shee shares of he muual fund valued S i.e. he marke value of he conrac a each dae, he valuaion problem can be summarized by : ( K ) S + 1[ > ] 1[ > ]. L A.

5 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN Revenue srucure Insead of charging a single up-fron premium as for radiional life insurance, hese kind of guaranees are financed hrough insallmens i.e. regular fees proporional o he marke value of he conrac (as asse managemen fees). Anoher par of he revenue comes from he surrender charges associaed wih early wihdrawals. he level of hose penalies essenially depends on he legislaion and he produc design. For he sake of simpliciy and conservaism he model described in his aricle will no ake ino accoun his source of revenue for he insurance company... he Model he framework for modeling hose guaranees is a coningen claim framework...1 Capial Markes facors Financial markes are assumed o be fricionless and complee. Under hese condiions Harrison and Kreps (1979) have shown here is a unique probabiliy measure Q, called risk neural probabiliy, under which he coninuously discouned price of securiies is a maringale. Muual fund process Le S be he value of he marke value of a uni of muual fund a ime. Under Q, we assume ha S is deermined by he following sochasic differenial equaion: ds = (r ϕ )S d + ρσ S S dz + 1 ρ σ S S dy Eq 1 S 0 σ S is he insananeous sandard deviaion of he reurn on muual fund and ρ is he correlaion coefficien beween he muual fund and he risk-free ineres rae. Z and Y are independen sandard Wiener processes. Ineres rae process We will use he classical one facor HJM model wih a consan volailiy explained by Heah, Jarrow and Moron (199) ha allows us o inegrae he curve as he one ha is observed in he marke. Under he risk neural probabiliy we assume: r = f( 0,) + σ r σ ry Eq Where f ( 0, ) is he insananeous rae given by he marke, and σ r is he insananeous sandard deviaion of he nominal raes... Acuarial facors Moraliy

6 17 F. PERNOUD & h. FAVRE-BONVIN For convenience and simpliciy we assume ha he age-a-deah random variable can be expressed in a coninuous-ime manner. hus, for an individual aged x, he probabiliy of deah afer ime 0 i.e. afer age x +, can be wrien as: where ( ) x λx ( s) ds P = e 0, ( ) A λ is called he hazard rae funcion. Wihou loss of generaliy he hazard rae funcion can be fied o a moraliy able. Obviously we assume ha Lapsaion is independen of ( ) A S,. Modeling wihdrawing behavior is a ricky exercise. I is very emping o ry o model lapse raes joinly depending wih ineres raes and muual fund performance. However such models are more complex o implemen and undersand and our focus is on models ha have shown hemselves able o manage GMAB risk in pracice. For conservaism sake we assume ha he ime-a-lapse random variable expressed he same way as moraliy: and ha L ( ) is independen of (,r ) δ P = e 0 L S.,A.3 Valuaion of he Asse-Liabiliy sysem ( s) ds r A L can be We presen in his par he valuaion a he policyholder level. A a porfolio level, he valuaion consiss in summing he head by head values. Le s define P (, ) he price a ime of a zero coupon defaul free bond wih a nominal 1 mauring a ime (wih ). r d f(,u)du P(,) = E = Q e e. MM Naked Le s define he 3 following variables: R : Presen Value of he revenue side (Asse) L : Presen Value of he claim side (Liabiliy) = R L is he ne posiion, also called mark-o-marke value of he GMAB (Naked refers o he fac ha i is no relaed o he ALM sraegy).

7 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN Revenue valuaion We assume ha all he fees are calculaed along he year (coninuously) based on he marke value of he invesmen, bu we assume ha his amoun is cashed only a he end of each calendar year. We will suppose here ha we receive our revenue (α annual premium rae) based on he accoun value of each policyholder in a yearly basis. Le be he mauriy of he guaranee and N he number of corresponding years. i N r d N ϕd ( δ(s) + λ(s) ) ( 0) = EQ α e 0 Si 1[ > i] 1[ > i] = αs e 0 0 e R 0 L A i= 1 i= 1.3. Liabiliy valuaion i i ds Eq 3 We assume here ha he mauriy of he guaranee is and he level of he guaranee is a fixed amoun K (ypically K = S 0 ) as follow: r d L( 0 ) = EQ e 0 1 L = e ( δ(s) + λ(s) ) 0 ( K S ) + 1[ > ] [ > ] ds r d EQ e 0 ( K S ) + A Eq 4 Le us define a new probabiliy measure, called -neural forward probabiliy define r ds dq e 0 = Eq 5 dq P( 0,) So we can rewrie under r σ = f( 0,) + Q boh equaions (1) and (): r σ r ( ) σ r Z Eq 6

8 174 F. PERNOUD & h. FAVRE-BONVIN S = S σs² ² ru ϕu du ρσsσr + σs 0e 0 ( ρ Z + 1 ρ²y ) Eq 7 A his poin we have all he elemens o evaluae he Liabiliy componen: ( δ(s) + λ(s) ) [( K S ) + ] L( 0 ) = P( 0,)e 0 EQ. We know from he las relaionship ha following parameers: ds S() ln is Normally disribued wih he S( 0 ) m() = (f( 0,u) ϕ u )du σ r σ S ρσ Sσ r (Mean) Var() = σ S + ρσ Sσ r + σ r (Variance). 3 So we can explicily wrie he value of he payoff funcion: ( δ(s) + λ(s) ) ds 0 K N( d ) P( 0, ) S N( d1) e L( 0 ) = e 0 0 ϕs ds Eq 8 d K ln m() S( 0 ) =, 1/ Var() 1/ d1 = d Var()..3.3 Global valuaion If we assume ha MM (0) represens he mark-o-marke value of he asse and Naked liabiliy aached o a given policyholder a incepion we can conclude ha: i N MM Naked( 0 ) = αs e 0 0 i= 1 e 0 ( δ(s) + λ(s) ) ( δ(s) + λ(s) ) i ds ϕ sd e 0 ds ϕ s KN(d )P(,) S N(d )e ds Eq 9

9 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN 175 Special case: For any given ime 0 i is sraighforward o expand his formula. For an illusraive and pracical sake, if we assume ha: Fees are consan: ϕ = ϕ Lapse raes are consan: δ = δ Moraliy follows a able { l x } hen Eq 9 becomes: N l (0) x i + MM Naked = αs0 + e + e KN ( d) P(0, ) S0N( d1) e i= 1 lx l. x Conex.3.4 Numerical example ( ϕ δ ) i lx δ ϕ ( ) he muual fund is supposed o be an indexed fund ha racks he CAC 40, assuming ha all dividends of he sock are insananeously reinvesed, and all he fees are aken coninuously from he fund. We assume ha we can represen all he policyholders by a single synheic person wih he following characerisics: Acuarial assumpions Age: 50 years old Sex: 50% male-50% female Moraliy able: French cerified able Lapse assumpion : annual exponenial rae 3% Ne single Premium: Insurance Policy erms Mauriy: 8 years Guaranee: 100% of he ne single invesed premium Fees: asse managemen + insurance loading + cos of guaranee = 3%/year Capial Marke assumpions: Ineres raes srucure: fla r =5% Muual fund volailiy: σ S = 3% Solving MM ( 0 ) = 0 comes up wih a fair price for α of 166bps i.e. charging Naked 1.66% per annum for he guaranee allows he risk-aker o balance a incepion he value of fuure premiums and he value of he guaranee. Now, le us imagine ha he equiy marke falls immediaely by % and he enire curve is shifed down by 0bps. hen he marke value of he ransacion (asse liabiliy)

10 176 F. PERNOUD & h. FAVRE-BONVIN becomes: i.e. 1.03% of he invesed premium. A his poin he fair price is now 183bps. 3. RISK MANAGEMEN Secion provides wih a comprehensive valuaion ool ha allows he risk-aker no only o se he price of a UL guaranee bu also o value he produc a any poin in ime. o his exen i is an ALM ool. As shown in he numerical example, seing a fair price a incepion doesn remove he risk. he whole A/L sysem has a high sensiiviy o capial marke environmen and has o be managed hrough ime. he purpose of his secion is o provide wih a clear quanificaion of he differen source of risk and heir conribuion o he enire sysem. hen we will show he efficiency of a classical -sraegy and is conribuion o he whole risk reducion. 3.1 Sources of Risk Before presening our risk managemen sraegy, we wan o underlines clearly where he risk is coming from. Financial Risk - Muual fund performance σs² ² ru ϕu du ρσsσr + σs S = S0e 0 - Ineres rae performance Acuarial Risk - Deah uncerainy r r σ = f( 0,) + i Q X ( σ r (. ( ρ Z + 1 ρ²y ) ) σ d) = Q ( d) + σ *H (d). i X QX - Lapsaion facor uncerainy i i L( d) = i L( d) + σ P*Z (d). Of course wih our simple models for Acuarial Risk i is heoreically possible o obain negaive lapse and moraliy raes. Bu we have found his o be he case in pracice when working wih some daabases. 3. Naure of he Risks GMAB is a porfolio of simple opions whose mulipliers are deermined by acuarial bes esimaes of fuure lapse and moraliy. As such a GMAB posiion will possess all he greeks or insananeous risk measures of a simple opion will. hese measures like rho and dela are valid for only an insan in ime and for infiniesimally small moves. Useful as hese figures are hey can no provide much insigh ino some basic and simple quesions. i r Z..

11 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN 177 Wha is he relaive sensiiviy of he GMAB posiion o ineres raes and equiies moves in he markeplace? o answer his quesion one can consruc a wo-way able of one-monh sandard deviaions moves in he underlying asse and he 8-year Swap rae and hen reevaluae our GMAB under hese new condiions holding everyhing else consan. o explore he naure of he risk of our simple GMAB we will examine he discouned Profi & Loss disribuion, is sensiiviy in a wo way able and is Greeks. P\L analysis We can ry o capure he risk by Mone Carlo simulaed all he risky parameers, and look a he disribuion of he discouned P\L. A his sep we only inroduce, he Underlying asse source of risk, assuming an iniial deposi of P\L disribuion Sd. Dev = Mean =.0 N = I appears ha he risk profile is asymmeric and ha large poenial losses can occur. Marginal conribuions o risk Wha is he conribuion of each facor o he overall risk profile? We define he marginal conribuion o risk by is conribuion o he global variance: Var(P\L ) C i source(i) = Var(P\L ). global wih i being a source of risk among he four previously described sources of risk. o ge he overall picure, we use accurae sochasic parameers coming from he capial marke place and acuarial sudies.

12 178 F. PERNOUD & h. FAVRE-BONVIN Risk Facors Conribuion o risk Underlying Asse 70% Ineres Rae 4% Lapse 5% Moraliy 1% his simple analysis underscores he financial risks associaed wih a GMAB. Unlike radiional Life Insurance producs GMAB guaranees are mainly driven by sysemaic risks. wo way able his able presens he value of ( 0) MM as a percenage of noional wih a 8- year swap rae moving from 4.8% o 5.% and an accoun value moving from 95 o 105. AV\IR 4.8% 5.0% 5.% % -1.5% -1.0% % 0.0% 0.4% % 1.% 1.6% his able shows how volaile he value of a GMAB is and how complex he risk profile is. Greeks Greeks are he sandard quaniaive measure for such complex risk profiles. We use he assumpion of he numerical applicaion o come up wih quaniaive values of he Greeks. Dela 6.93% Rho Vega -57 Gamma 0 he Dela and he Rho quanify he sysemaic risks of a sandard GMAB a incepion. 3.3 Hedging a GMAB One way an insurance company can hedge he risk of a GMAB is o buy pu opions wih he same mauriy as he GMAB. One problem wih his approach is figuring ou exacly how many pus o buy in pracice because he correc amoun depends of policyholder behavior and on erminal fund performance. A second problem wih his approach is realizing i fails immunize he revenue sream of a GMAB he very hing ha Naked

13 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN 179 will finance he upfron cos of buying pus in he firs place. Anoher pracical problem wih his risk managemen echnique is he volailiy i inroduces in he financial resuls under mark-o-marke accouning. We advocae, based on our experience, using a dynamic hedging program o minimize he volailiy of a GMAB s profi. his approach is consisen wih bes oucome for hedging as bes hedge can be pu in place when new informaion arrives regarding policyholders, fund performance and capial marke changes. For us a pracical hedging sraegy would consis of removing sysemaic equiy risk and conrolling ineres rae risk using fuures. I is our view a real ime risk and rading sysem should be in place in order o properly manage hese risks. We also sugges ha a hedged GMAB be a GMAB wih an appropriae surrender charge schedule as his can miigae he hedging problem creaed by raional lapse behavior. In order o assess how his dynamic hedging sraegy conribues o minimize he volailiy of he P&L, we simulaed he P&L including a naïve Dela neural sraegy wih a weekly rebalancing. he following graph shows he disribuions of boh naked and hedged P & Ls under Black & Scholes universe. pdf NPV (P&L) Hedged vs Naked under RN capial markes universe 10,000 scenarios 40% 35% Hedged Naked 30% 5% 0% 15% 10% 5% -60% -50% -40% -30% -0% -10% 0% 10% 0% 30% 40% 50% P&L 0%

14 180 F. PERNOUD & h. FAVRE-BONVIN In his simple es i is clear ha he volailiy and shape of he erminal disribuion is dramaically alered. herefore i becomes possible for an Insurance company o se a price such as he probabiliy of ruin is minimized. 3.4 Reserves & Capial mehodology Reserves Mos of he sandard mehods for reserves valuaion are moving o he banking sandard or he mark-o-marke sandard. In case of hedging we advocae he reserve being equal o he overall ne posiion which includes he mark-o-marke value of he naked GMAB and he hedge porfolio Reserve() = Min( 0,MMnaked() + HedgingPorfolio( )). Noe how wih our simple example his reserve figure can be quickly arrived a in pracice on a large number of policyholders as no simulaion work is required Capial How should capial be se for Hedged GMAB business? Whaever he mehodology i should reward companies ha are hedging effecively. We feel a simple measure and a simple rule are he bes. Our simple measure of hedging effeciveness is he r-squared based on a regression of he cumulaive weekly changes in he hedge porfolio on changes in he GMAB or naked porfolio. We hen considered hedging o be efficien if our hedging effeciveness measure was greaer han.65. In oher words he hedge porfolio could explain a leas 65% of he variabiliy in he weekly changes in he GMAB s value. We sugges on a quarerly basis hedging effeciveness be measured and capial be reallocaed. How do we assess Capial requiremen? A his poin all we have said is ha capial for GMAB should be relaed o hedging and only if hedging is acually efficien in pracice. We sill need o discuss wha we feel is an appropriae echnique o assess capial on unhedged GMAB business. All he mos common echniques such as Value a Risk are suffering when he normaliy disappears, and in our case if you pu uncerainy on moraliy or lapsaion, we loose his propery. o capure all he exreme evens, we hink ha he Condiional ail Expecaion (CE) will be appropriae. he concep of CE o deermine capial is quie inuiive, he capial required is precisely he expeced shorfall when a shorfall occurs (Arzner e Al. 1999). However using a ail measure is always a challenge as far as i requires MC simulaion echniques. o capure he accuracy of a CE measure a confidence inerval is necessary.

15 MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN 181 Applicaion o our problemaic he Office of he Superinenden of Financial Insiuions in Canada (OFSI) recenly imposed sric rules concerning capial allocaion for produc like ours. he insurer mus allocae capial define by he CE a 95%, if no hedging is pu in place. In case of hedging sraegies, he insurer can reduced he OFSI capial requiremen up o a maximum of 50% of his amoun. Remarks Why 50%? Why would people hedge knowing hey will only ge 50% credi for? We advocae a conservaive and less capricious approach o capial requiremen. 1 OSFI: C = CE95% ( Naked ) CE95% ( Naked ) CE95% ( Hedged) Re ( ) serves Proposed Capial Requiremen: = ( 1 R ) CE ( naked ) wih being he realized C 95% R defining Hedging Efficiency. If he insurance or reinsurance company is no hedging he produc he equal o zero, so he Capial requiremen will be he same as he OSFI one. R will be A incepion he capial deploymen will be he same, if you re hedging or no. Why is i a good hing? he model can lead o a perfec resul bu he realiy can be oally differen, especially for people ha ry o bea hedge acively managed funds. Our conservaive mehod is designed o proec he policyholder. he capial requiremen is direcly linked o he Hedging effeciveness in pracice and no o heoreical projecions of hedging. 4. CONCLUSION he main goal of his documen was o provide an uniform valuaion echnique for he GMAB produc, ha is consisen wih capial markes risk managemen. Mos of he ime people only price he Equiy risk bu forge he impac of ineres rae deviaion; using HJM framework allow people o incorporae his elemen in heir pricing arge. Our recommendaion for risk managemen concern is simple : Life insurers should srucure GMAB in such ways ha he lapsaion risk is paid by he policyholder using surrender charges and ha he financial risks are ransferable o he capial marke place hrough dynamic hedging sraegy. he accouning rules for hose producs should reward risk managemen sraegies, ha are differen from he classical echniques of Life insurers

16 18 F. PERNOUD & h. FAVRE-BONVIN promoing he fac ha new sales offse he effec of a bad block of business. his is key o encourage Life insurer o adop he righ aiude. We describe in his paper valuaion echniques for reserve and capial ha can be used by any Life insurers using or no risk managemen sraegies. GMABs are a major innovaion in he field of guaraneed producs (GPs). Like all guaraneed producs, hey offer a proecion or a guaranee o invesors on heir capial and an upside o he performance of a risky asses. GMABs differ from radiional srucured GPs ha are available in Europe from he invesor s poin of view as hey offer : - ransparency: he underlying securiy for a GMAB is an index fund compared o a porfolio of zero coupon bonds and opions in srucured GP. Wih a GMAB he guaranee and is associaed volailiy is effecively sripped ou from he invesor s securiy. - Flexibiliy: wih a GMAB an invesor can wihdraw his money a any ime wih a visible price for a known surrender charge versus a srucured GP produc where a special price mus be made for he clien We can exend our mehodology and echniques o he Guaraneed Minimum Deah Benefi (GMDB) sold over he world aggressively he las 10 years. he only difference beween hose wo producs is he rigger of paymen. ha is why you can exend he «mark-o-marke» mehodology and is associaed risk managemen sraegies o he GMDB producs. Afer he 00 bearish Equiy marke, mos of he Life insurer have o find risk managemen sraegies o avoid fuure volailiy in heir balance shee as well as o eliminae all he downside equiy risk.

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