Securitization and Tranching Longevity and House Price Risk for Reverse Mortgages

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Securitization and Tranching Longevity and House Price Risk for Reverse Mortgages"

Transcription

1 Securiizaion and Tranching Longeviy and House Price Risk for Reverse Morgages Sharon S. Yang 1 Absrac Reverse morgages are new financial producs ha allow he elders o conver heir home equiy ino cash unil hey die. From he provider s perspecive, longeviy risk and house price risk are he major risks involved wih reverse morgages. This paper proposes a securiizaion mehod o ransfer he risks associaed wih reverse morgages and focuses on ranching longeviy and house price risks for differen invesors. The srucure of securiizaion for reverse morgages is similar o ha for collaeralized deb obligaion(cdo). Differen o price CDO, we model he dynamics of fuure moraliy and house price insead of defaul rae. Thus, we model he house price index using ARMA-GARCH process. To deal wih longeviy risk for elders, we use he CBD model (Cairns e al, 2006) o projec fuure moraliy. We propose a risk neural valuaion framework and employ he condiional Esscher ransform o price he fair spreads for differen ranche invesors. The problems of using saic moraliy able and model risk on pricing fair spread are invesigaed numerically. Keywords: Reverse morgage; GARCH Process; Esscher ransform 1 Deparmen of Finance, Naional Cenral Universiy, Taoyuan, Taiwan. 1

2 1.Inroducion Human longeviy has been increasing significanly since he sar of he 20h cenury. Wheher human longeviy will coninue o improve in he fuure is debaing. The view ha longeviy will coninue o increase is suppored by he moraliy experience in many developed and developing counries (Tuljapurkar e al., 2000; Blake e al., 2008; Yang e al., 2009). Thus, how o increase he reiremen income o mainain he elder s living sandard has become an imporan issue. The pension sysem was he main financial resource for he elders o spend for life. Due o he phenomenon of ageing populaion and increases in longeviy, he pension and annuiy providers are suffered subsanial financial problem and sar o reduce he pension benefi in response (Anolin, 2007; Bauer and Weber, 2007). Governmens are now facing a grea challenge for financing an ageing populaion. Therefore, he developmen of innovaive financial producs in privae marke o increase reiremen income is needed. Home equiy has been found o be a major asse of individuals in many counries a reiremen. For example, in Ausralia 2, oal owner-occupied home equiy was AUD$887 billion wih hose over he age of 60, accouning for AUD$345 billion (39%) of his amoun; in he US, he American Housing Survey 3 shows ha more han 12.5 million elderly have no morgage deb, and he median value of morgaged-free homes is US $127,959. Reverse morgage is a new financial produc ha allows he elders o conver a proporion of he equiy in heir home ino cash unil hey die. Kuy(1998) indicaes ha he use of home equiy conversion morgage 2 Senior Ausralians Equiy Release Associaion of Lenders Indusry Submission, American Housing Survey for he Unied Saes (2005), Curren Housing Repors, H150/05. US Deparmen of Housing and Urban Developmen and US Census Bureau, Aug. 2006, P156. 2

3 producs could possibly raise abou 29% of he poor elderly homeowners in he U.S. above he povery line. In he Unied Saes, he deparmen of Housing and Urban Developmen (HUD) firs inroduced he Home Equiy Conversion Morgage (HECM) program in In addiion o he U.S. marke, reverse morgage producs are also found in he U.K., Ausralia and in Asian counries of Singapore and Japan. Reverse morgages differ from radiional morgages in he way ha he loans and accrued ineress are repaid once when he borrower dies or leave he house. Unlike radiional morgage pools, he credi risk in reverse morgage pools is no driven by poenial defaul of he loans. The main risk facors are he moraliy, ineres rae and he value of he underlying propery. If a borrower lives longer han expeced or he decrease in house price, he principal advances and ineres accruals may drive he loan balance above he proceeds of sale he propery. Thus, reverse morgage is considered o be longeviy dependen asse. To develop reverse morgage producs, risk managemen has become imporan for he RM provider o conrol and manage he risk. Tradiional mehods for dealing wih he risks associaed wih reverse morgages are using insurance or wriing no-negaive guaranee. For example, he HECM program in he Unied Saes. The borrower pays a fron fee of 2% of he iniial propery value as he iniial propery value. The lenders under his program are proeced agains he losses arising when he loan balance exceeds he equiy value a ime of selemen. In Briain, mos of roll-up morgages are sold wih a no-negaive-equiy-guaranee (NNEG) ha proecs he borrower by capping he redempion amoun of he morgage a he lesser of he face amoun of he loan and he sale proceeds of he home. The NNEG can be viewed as a European pu opion on he morgaged propery. Li e al.(2009) develop a framework for pricing and managing he risks for he NNEG. 3

4 Securiizaion is a new financial innovaion o hedge longeviy risk. Blake and Burrows (2001) were he firs o advocae he use of moraliy-linked securiies o ransfer longeviy risk o capial markes. The EIB/BNP longeviy bond was he firs securiizaion insrumen designed o ransfer longeviy risk bu was no issued finally and remained heoreical. Survivor swaps, survivor fuures and survivor opions have been sudied by boh academics and praciioners (Blake e al., 2006; Dowd e al., 2006, Biffis and Blake, 2009; Blake e al. 2010). The firs derivaive ransacion, a q-forward conrac, was issued in January 2008 beween Lucida 4 and JPMorgan (Coughlan e al., 2007); he firs survivor swap execued in he capial markes beween Canada life and a group of ILS and oher invesors in July In his conex, he valuaion of moraliy-linked securiies represens an imporan research opic for he developmen of capial marke soluions for longeviy risk. Securiizaion of longeviy risk for annuiy business and pension plans have been widely discussed (Macminn e al., 2006; Michael and Wills, 2007 ). Securiizaion of reverse morgage is sill in he early developing sage (Zhai, 2000). Wang e al.(2007) illusrae a securiizaion mehod o hedge he longeviy risk inheren in reverse morgage producs. They sudy boh of survivor bonds and a survivor swap and demonsrae ha securiizaion can provide an efficien and economical way o hedge he longeviy risk in reverse morgages. Sherris and Wills(2007) poin ou ha srucuring of longeviy risk hrough a special purpose vehicle requires consideraion of how bes o ranche he risk in order o mee differen marke demands. The exising lieraure illusraes he srucure and pricing longeviy bond for annuiy business(liao e al. 2007; Wills and Sherris, 2010) no for reverse morgages. This aricle aemps o fill his gap. We furher consider he ranche design of longeviy 4 A UK-based pension buyou insurer. 4

5 securiy for a porfolio of reverse morgages and illusrae he pricing of fair spreads for differen ranche invesors. The srucure of he securiizaion for longeviy risk is similar o he collaeralized deb obligaion (CDO) for credi risk. Thus, we call i as a collaeralized reverse morgage obligaion (CRMO) in his research. Differen o he survivor swap, he design of CRMO consiss on ranching and selling he risk of he underlying porfolio of reverse morgages. The lender of reverse morgages, invesmen bank or insurance company, decides o buy proecion agains he possible losses due o he longeviy risk of he underlying borrower (homeowner). The special purpose company designs he securiy wih he payoff depending on he uncerainy of fuure losses on he underlying reverse morgage and ranche he risks o differen invesors. To price he fair spread of CRMO for differen ranches, we assume a pool of reverse morgages. Among he reverse morgage produc in he US marke, he home equiy conversion morgage(hecm) program is considered he mos popular one, which accouns for 95% of he marke (Ma and Deng, 2006). Thus, we assume he pools of loans are under he HECM program. To model he loss for HECM program, we need o consider boh longeviy risk and house price risk. The CBD model (Cairns e al., 2006) is used o capure he dynamic of fuure moraliy for borrowers. To capure he properies of auocorrelaion and volailiy clusering ha are found in he lieraure(crawford and Fraanoni, 2003; Miller and Peng, 2006; Chen e al., 2010), we employ ARMA-GARCH process o model he house price dynamic. The risk neural pricing framework for he CRMO is derived using condiional Esscher ransform. Since moraliy modeling plays an imporan role in pricing longeviy securiies, we also sudy he impac of moraliy modeling on pricing he fair spread for CRMO. We consider he Lee-carer model(1992) o calculae he resul. In 5

6 addiion, he earlier HECM program uses saic moraliy ables o calculae he loan value. We also invesigae he effec of failing o capure he dynamics of moraliy on securiizaion of longeviy risk for reverse morgages, The srucure of his paper is organized as follows: 2. Modeling he Risks for HECM Program 2.1 HECM Program In he US marke, HECM program, Fannie Mae's Home Keeper program, and Financial Freedom's Cash Accoun Advanage are hree major reverse morgage programs. HECM Program was auhorized by Deparmen of Housing and Urban Developmen (HUD) in he Housing and Communiy Developmen Ac of Because he HECM program is insured by he US federal governmen, i is he mos popular reverse morgage program and accouns for 95% of he marke (Ma and Deng, 2006). Under he HECM program, he borrower mus be a leas 62 years age, living in a single family propery ha mees HUD s minimum propery sandard. The loan can be aken as four common repaymen forms including lump-sum, line of credi, enure, and erm. The iniial loan amoun ha can be borrowed depends on he iniial loan principal limi (IPL), which is decided according o he borrower s age, propery value and ineres rae. From he lender s perspecive, he loss occurs when he borrower lives longer han expeced or he decrease in house price, he principal advances and ineres accruals may drive he loan balance above he proceeds of sale he propery. To 6

7 proec he lenders from possible losses, HUD provides morgage insurance for he HECM program. The morgage insurance premiums are paid by borrowers and include an upfron premium of 2% of he adjused propery value and an annual rae of 0.5% of he loan ousanding balance as long as he loan is acive. Differen o morgage insurance, in his research, we propose a securiizaion mehod o hedge longeviy risk for reverse morgage producs. Therefore, we illusrae using he HECM program. 2.2 Major Risks in HECM Program Reverse morgages differ from radiional morgages in he way ha he loans and accrued ineress are repaid once when he borrower dies or leave he house. Thus, unlike radiional morgage pools, he credi risk in reverse morgage pools is no driven by poenial defaul of he loans. Longeviy risk, ineres rae risk and house price risk are he major risks for reverse morgages. If he borrower lives longer han expeced, he principle advance and ineres will coninue o accumulae. I may cause he ousanding balance excess he proceeds from he sale of he propery. Thus, he lenders of reverse morgages are faced wih longeviy risk. A risk in ineres raes can cause higher ineres on he ousanding balance. Thus, i increases he risk ha ousanding balance excesses he propery value. If he propery value decreases, i also increases he risk ha ousanding balance excesses he proceeds from he sale of he propery. Tha s called house price risk. In his research, we focus on he longeviy risk and house price risk for reverse morgages. 2.3 Modeling Possible Losses for HECM Program Le H denoe he propery value and OB represen he loan balance a ime. If he loan is due a ime, he possible loss can be expressed as 7

8 ( ) L = max OB H,0, for = 1 ~ ω x (2-1) where ω is maximal survival age. We consider he loan is due only when he borrower dies in ha year. Thus, he presen value of expeced oal loss a ime 0 is hen calculaed as ω x TL(0) = E[ e p q L ] = 1 r 1 x x+ 1 (2-2) where 1 pxdenoe he survival probabiliy ha he borrower aged x and survives o age x+-1, q x + 1 is he probabiliy ha he borrower dies in year. To ransfer he longeviy and house price risks for HECM program, we need o consider boh moraliy dynamic and house price dynamic, which are described below. 3. Modeling longeviy risk To examine he effec of longeviy risk for reverse morgages, we need a sochasic moraliy model o capure fuure moraliy dynamics properly. Various moraliy models exis; for example, early developmens of sochasic moraliy modeling rely on he age-period effec and pioneering work by Lee and Carer (1992) and Renshaw and Haberman (2003) offer furher analyses of he Lee-Carer model. Cairns e al. (2006a) insead consider heir CBD model of funcional relaionships, which deals wih moraliy raes across ages and hus offers beer performance for older persons. The CBD model also has been adaped o effors o price longeviy bonds or oher moraliy-linked securiies. In line wih he mos recen lieraure on moraliy modeling, we employ CBD sochasic moraliy o model longeviy risk for reverse morgage and calculae he fair spread for he proposed securiy. 8

9 3.1 The CBD model The CBD moraliy model we used was proposed in Cairns, Blake, and Down (2006). They sugges a wo-facor model for modeling iniial moraliy raes insead of cenral moraliy rae. The moraliy rae for a person aged x in year ( qx (, )) is modeled as follows: 1 2 logi qx (, ) k k ( x x) = + (3-1) where parameer 1 k represens he marginal effec wih imes on moraliy raes and parameer 2 k porrays he old age effec on moraliy raes and x is he mean age. The fuure moraliy can be projeced 3.2 Parameer esimaes We esimae he parameers in he CBD model by fiing hisorical U.S. moraliy daa from wih he HMD daa. The esimaed parameers of k 1 and 2 k for males and females are depiced in Figure 1 and 2. 1 k shows a down rend and 2 k appear a upward rend. To projec fuure moraliy raes, we model follows. k 1 and 2 k as () () 1 1 (1) κ mu1 κ 1 e = + ( 2) ( 2) (2) κ mu + e 2 κ 1 (3-2) 9

10 kappa1 kappa Year Year Figure 1. Esimaed Values of kappa1() and kappa2() of Male, 1950 o kappa1-2.8 kappa Year Year Figure 2. Esimaed Values of kappa1() and kappa2() of Female, 1950 o A Comparison of Projeced Moraliy Raes Moraliy modeling plays an imporan role in longeviy securiizaion. We also 10

11 examine he longeviy risk modeled by he Lee-Carer model (Lee and Carer, 1992) o invesigae he effec of model risk on securiizaion for reverse morgages. The Lee-Carer (LC) model is emerging as a benchmark for moraliy forecass. To undersand he disincion among he CBD, LC moraliy models and saic moraliy raes, we compare he simulaed survival probabiliy for a man aged 62 years separaely in Figure 3, which shows he survival probabiliy projeced by he CBD model is greaer han ha offered by he LC model. Since he saic moraliy raes ignoring he moraliy improvemen, he projeced survival probabiliy is much underesimaed. Figure 3. Simulaed Survival Probabiliy for American Males 4 Modeling Housing Price Dynamics 4.1 The House Price Daa Chen e al(2010) deal wih HECM program and choose he naionwide house price index(hpi) o model he house price dynamics. We use he same house price daa and exend he daa period from he firs quarer of 1975 o he firs quarer of 11

12 2010. Le Y denoe he log-reurn for house price index, which is defined H asy = log( H ). Based on he empirical HPI daa(see Figure 4), he log- reurn of 1 HPI is no saionary 5 and he firs difference of log- reurn( DY ) is saionary. Thus, we model he house price reurn based on he firs difference of log- reurn, which is calculaed asy Y 1. Figure 4 Log-reurn of HPI from 1975/Q1 o 2010/Q1 4.2 ARMA-GARCH Process Li e al.(2010) poin ou hree imporan properies for he house price dynamics in he U.K, which are auocorrelaion, volailiy clusering and leverage effecs. Based on he naionwide HPI in he U.S., he leverage effec doesn exis. Therefore, we consider he propery of auocorrelaion and volailiy clusering o model he house price reurn dynamic and employ he ARMA-GARCH process. The model is expressed as 5 Boh he ADF saisic and he PP saisic in CSXR are higher han he criical values a he significance level of 5%. 12

13 Under ARMA-GARCH model seing, he dynamics of house price reurn process is (4-1) (4-2) 4.3 Parameer Esimaes Based on he empirical daa, we find he ARMA(2,0)-GARCH(1,1) model gives he bes fi o he HPI daa 6. The parameer esimaes are presened in Table 1. Table 1 Parameer Esimaes for ARMA(2,0)-GARCH(1,1) Process Parameers Esimae Sd. Error value Pr(> ) φ E-06 φ E-07 2 α E α β E The Srucure of Securiizaion for Reverse Morgages and Valuaion of CRMO 3.1 The Srucure of Securiizaion for Reverse Morgages We propose a ranching securiy ha he srucure is similar o collaeralized deb obligaion(cdo). A CDO is an asse backed securiizaion where he underlying porfolio is comprised of securiies (called a Collaeralized Bond Obligaion, CBO) or 6 Chen e al.(2010) also find ARMA(2,0)-GARCH(1,1) gives he bes fi o he daa from 1975/Q1 o 2009/Q1. 13

14 loans ( called a Collaeralized Loan Obligaion, CLO) or possibly a mixure of securiies and loans. A CDO consiss on ranching and selling he credi risk of he underlying porfolio. We design a securiizaion where he underlying porfolio is a pool of RM producs, ha is called collaeralized reverse morgage oblighaion(crmo) in his research. The srucure of CRMO is described in Figure 1. The proecion buyer, invesmen bank, pays he premiums ( P ) o he proecion seller, special purpose vehicle (SPV). The SPV issues hree ranches of he CRMO o invesors wih differen degree of risk preferences. The oal face amoun of bonds issuing o invesor is equal o ( F ). SPV invess he premium ( P ) and he proceeds from he sale of bonds ( F ) in defaul-free floaing bonds wih coupon rae ( C )). If he loss ( L ) on he underlying RM produc occurs, he ranche invesor will receive he residual nominal value of conrac( F L ). Thus, he invesor will bear he fuure uncerainy of loss and need o be compensaed. The compensaion reurn is called spread. In his research, we invesigae he fair spreads for differen ranche invesors. Residual Nominal Value Provider of RM Premium( P ) Paymen ( L ) Nominal Value of Conrac ( P ) SPV of Conrac ( F L ) Tranche Premium ( R () = P+ c ()) Coupon ( () c ) Nominal Value of Conrac ( F ) Senior S Tranche ( F, r %) Mezzanine M Tranche( F, r M % Equiy E Tranche( F, r %) E S Collaeral (Defaul-free floaing bonds) 14

15 Figure 1 The Srucure of CRMO The SPV disribues he sales of bond o each ranche according o he ranching proporion( S%, M%, E %), ha is S % of oal face amoun o Senior ranching invesor, M % o Mezzanine ranche invesor and he res o he Equiy ranche invesor. The corresponding face amouns and fair spread for hese hree ranches are S M E denoed as ( F, F, F ) and ( r %, r %, r % ) separaely.. Differen ranche S M E invesors receive differen spreads. A ime, when he loss occurs, he equiy ranche firs absorbs he loss and he face amoun decreases he same amoun. If he loss is larger han he residual face amoun in he Equiy ranche, he Mezzanine ranche has o be responsible for he loss. The Senior ranche is he las o absorbing he loss. The fuure residual face amoun in Equiy, Mezzanine and Senior ranches a ime can be expressed as F if 0 L E E E E + 1 = if 0 < E 0 if L > F F F L L F F if L F M E M M E M + 1 = if < M 0 if L > F F F L F L F F if L F S M S S M S +1 = if < S 0 if L > F F F L F L F For he invesor s poin of view, he equiy ranche firs absorbs he loss. Thus, he invesor s in equiy ranche is he mos risky invesor comparing wih ha for Mezzanine ranche and Senior ranche. 3.2 Valuaion of Collaeralized reverse morgage obligaion(crmo) 15

16 We propose a risk neural valuaion framework o find he fair spread for differen ranche invesors.. Based on he underlying porfolio of RM policies, he oal losses are modeled according o Equaion(2.1). Assume he loss occur a he middle year. A ime 0, he presen value of he expeced oal loss absorbing by Equiy ranche invesor is calculaed as ( 1 ) T r ( 0.5) E E E(0) = Q[ ] = 1 where r is he risk free rae, ( E E F 1 F ) L e E F F (3-1) denoes he acual loss a ime ha absorbed by Equiy ranche and EQ[] represens he expecaion under risk neural measure. The presen value of he expeced oal compensaion received by he Equiy ranche invesor is expressed as T r E E E Q E 1 = 1 P (0) = e E [ r %( F + F 2)] (3-2) Thus, he fair spread( r E ) for Equiy ranche invesor can be obained by seing P (0) = L (0) (3-3) E E I implies ha he expeced oal losses absorbed and he expeced oal compensaion received by he Equiy ranche invesor shall be he same. The valuaion formula applies o Mezzanine ranche and senior ranche. In addiion, he presen value of expeced oal loss presened in Equaion(2-2) shall be equal o he oal losses absorbed in differen ranches, which is TL(0) = L (0) + L (0) + L (0) E M S (3-4) To calculae he risk neural measure for house price dynamics and moraliy dynamics, we employ he condiional Esscher ransform o price he fair spreads for differen ranche invesors. 16

17 5. Numerical Illusraion 5.1.Policy Seing for Reverse Morgages To illusrae he calculaion of fair spread for he ranching securiy of RM producs, we assume a porfolio of 1,000 idenical RM policies issuing o he borrower aged 62 wih iniial propery value of US$300,000 and loan aking in lump-sum paymen. The oal loan value is US$180,000,000. Assume he provider of RM wan o ransfer he enire risk. Thus, he SPV issues he bond wih oal face amoun equal o US$180,000,000. The example of ranche level and he disribuion of he face amoun o each ranche are shown in Table 1. Based on he ranche level, we invesigae he fair spread for differen ranche invesor. Table 1 Illusraion of Tranche Levels Level Face Amoun in Each Tranche Senior ranche 5% 900,000 Mezzanine ranche 10% 1,800,000 Equiy ranche 85% 15,300,000 Toal 100% 180,000,000 Following he HECM program and he policy seing in Chen e al.(2010), we consider he ransacion cos of selling he house(κ ) and renal yield( g ) in our numerical analysis. Assume κ = 5% and g = 2%. The ineres rae charged on he loan(i ) is assumed o be 2.42%. The moraliy model and he house price model used o model he possible losses are presened in Secion 3 and 4. The risk free rae is assumed o be consan and we use 3.78%. We carry ou 100,000 Mone Carlo Simulaions o calculae he numerical resuls Shorfalls Analysis for Issuing RM Producs 17

18 We firs analyze he shorfalls for he provider when issuing a porfolio RM Producs. Based on differen loan o values, Table 2 presens he shorfalls in erms of value a risk(var) and condiional ail expecaion(cte). As expeced, he higher he LTV, he higher he shorfalls. For he LTV equal o 90%, he probabiliy of no loss occurring is less han 1%(0.059% acually) and CTE(90%) is US$200,753 for females. Comparing he resuls wih ha of LTV equal o 50%, he probabiliy of no loss occurring is around 9.14% and, CTE(90%) is US$109,429 for females. The shorfall is much smaller. Thus, he LTV is very criical o he risk involved in issuing RM policy. Transferring he risk for RM provider is necessary especially for higher LTV. Table 2 Shorfall for a Porfolio of RM Policies LTV Gender Prob. of no Loss max mean VaR 90% VaR 95% VaR 99% CTE 90% CTE 95% CTE 99% (Loss=0) 50% Male % 117,348 67, , , , , , ,724 Female % 115,747 67, , , , , , ,429 60% Male % 141,360 85, , , , , , ,941 Female % 138,938 85, , , , , , ,916 70% Male % 165, , , , , , , ,490 Female % 162, , , , , , , ,640 80% Male % 190, , , , , , , ,324 Female % 185, , , , , , , ,578 90% Male % 214, , , , , , , ,519 Female % 209, , , , , , , , Analysis of Fair Spreads The fair spreads of CRMO for differen ranches are presened in Table 3. For a illusraion purpose, we calculae he fair spreads for boh male and female borrowers and differen LTV of 50%, 60%, 70%, 80% and 90%. Based on he LTV of 60%, he fair spread for Equiy ranche is 8.517%, for Mezzanine is % and for Senior is 18

19 1.5507% for male borrowers. Differen ranche invesors bear differen degree of risk. Since he equiy ranche invesor absorbs he loss firs han oher ranche invesor, he fair spread in equiy ranche is much higher han oher ranches. The fair spreads for he hree ranches are lower for female borrowers. This is because he life expecancy for female is longer. We furher compare he fair spreads for he underlying reverse morgage porfolio wih differen LTV. As expeced he higher he LTV, he higher he fair spread is. Since he higher LVT may resul in higher loss, he invesor needs o bear more risk and requires more compensaion. In addiion, he change in spreads is more significan for he Equiy ranche invesors and less significan for Senior ranche invesors. For he LVT of 50% o 90%, he fair spread changes from % o % for Equiy ranche invesors, more han 9.5% difference; bu from % o % for Senior ranche invesors, less han 1.5% difference. Table 3 Fair Spreads for Differen Tranches of CRMO ( λ = 1% ) LTV 50% 60% 70% 80% 90% RM Borrower Equiy Mezzanine Senior 5% 10% 85% Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % In able 4, he fair spreads are calculaed assuming he risk premium is 0.1. We invesigae he risk premium assumpion on he calculaion of fair spread. Table 3 19

20 presens he fair spread based on risk premium assumpion of 0, 0.1, 0.2 and 0.3. As expeced, he higher he risk premium in pricing, he lower he fair spread is. Howver, he effec is no significan. Table 4 The Effec of Risk Premium on Fair Spreads ( LTV = 60% ) Risk Premium λ = 0.0 λ = 0.1 λ = 0.2 λ = 0.3 RM Borrower Equiy Mezzanine Senior 5% 10% 85% Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Securiizaion longeviy risk for annuiy business has been widely discussed. The discussion of longeviy risk o reverse morgages is sill under developmen. The earlier HECM program uses saic moraliy ables o calculae he loan value. To invesigae he effec of failing o capure he dynamics of moraliy on securiizaion of longeviy risk for reverse morgages, Table 5 presens he resul using saic moraliy able 7. Comparing he resuls wih Table 3, he fair spread increases in each ranche. From he SPV poin of view, ignoring moraliy dynamic will overesimae he fair spread. Table 5 The Effec of Ignoring Moraliy dynamics on Fair Spreads for Differen Tranches of CRMO Equiy Mezzanine Senior LTV RM 5% 10% 85% 7 Based on HMD, we use he moraliy experience in year 2006 as he saic moraliy able. 20

21 50% 60% 70% 80% 90% Borrower Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Finally, we invesigae he fair spread based on differen moraliy model. We employ he LC model o calculae he fair spread. In mos of he cases, he fair spread based on LC model is lower. This is because he projeced life expecancy using CBD model is a lile bi longer han ha using LC model. Table 5 The Effec of Moraliy Model Risk on Fair Spreads for Differen Tranches of CRMO( λ = 1% ): LC model LTV 50% 60% 70% 80% 90% RM Borrower Equiy Mezzanine Senior 5% 10% 85% Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % Male % % % Female % % % 21

22 5. Conclusion In recen years, reverse morgages are geing more popular in many counries. To ransfer he risk inheren in reverse morgage producs, we propose a securiizaion mehod. The proposed securiizaion srucure differs from exising lieraure by inroducing he ranche longeviy and house price risks for reverse morgages. The srucure of securiizaion for reverse morgages is similar o ha for collaeralized deb obligaion (CDO). Differen o price CDO, we model he dynamics of fuure moraliy and house price insead of defaul rae. Thus, we model he house price index using ARMA-GARCH process. To deal wih longeviy risk for elders, we use he CBD model (Cairns e al, 2006) o projec fuure moraliy. We propose a risk neural valuaion framework and employ he condiional Esscher ransform o price he fair spreads for differen ranche invesors. The problems of using saic moraliy able and model risk on pricing fair spread are invesigaed numerically. In our numerical analysis, we firs analyze he shorfalls for he provider when issuing a porfolio RM Producs. We calculae he fair spreads for boh male and female borrowers and differen LTV of 50%, 60%, 70%, 80% and 90%. Since he equiy ranche invesor absorbs he loss firs han oher ranche invesor, he fair spread in equiy ranche is much higher han oher ranches. The fair spreads for he hree ranches are lower for female borrowers. This is because he life expecancy for female is longer. We furher compare he fair spreads for he underlying reverse morgage porfolio wih differen LTV. As expeced he higher he LTV, he higher he fair spread is. Since he higher LVT may resul in higher loss, he invesor needs o bear more risk and requires more compensaion. In addiion, he change in spreads is more significan for he Equiy ranche invesors and less significan for Senior ranche invesors. 22

23 The earlier HECM program uses saic moraliy ables o calculae he loan value. We also invesigae he effec of failing o capure he dynamics of moraliy on securiizaion of longeviy risk for reverse morgages. From he SPV poin of view, ignoring moraliy dynamic will overesimae he fair spread. In addiion, we employ he LC model o calculae he fair spread. In mos of he cases, he fair spread based on LC model is lower. This is because he projeced life expecancy using CBD model is a lile bi longer han ha using LC model. Thus, i implies he use of LC model will underesimae he fair spread o he invesors. In he ligh of our analysis in his paper, we also highligh some areas for furher research. Firs, we do no invesigae he issue of jump effec wih house price dynamic and moraliy raes. Second, we ignore sochasic ineres rae in he valuaion framework. Third, we only consider he reverse morgages in he form of lump-sum paymen. These hree areas would be valuable and ineresing exensions for addiional research o ackle. 23

24 Reference 1. Cairns, Andrew J.G., David Blake and Kevin Dowd (2006). A Two-facor Model for Sochasic Moraliy wih Parameer Uncerainy: Theory and Calibraion, Journal of Risk and Insurance, 73: Chen, Hua, Samuel H. Cox, Shaun S. Wang(2010).Is he Home Equiy Conversion Morgage in he Unied Saes susainable? Evidence from pricing morgage insurance premiums and non-recourse provisions using he condiional Esscher ransform. Insurance: Mahemaics and Economics 46:, David Blake, Anja De Waegenaere, Richard MacMinn, Theo Nijman, 2009, Longeviy Risk and Capial Markes: The Updae. 4. Lee, R. D. and L.R. Carer (1992). Modeling and Forecasing U. S. Moraliy, Journal of he American Saisical Associaion, 87: Li, J. S. H., M. R. Hardy and K. S. Tan(2010). On Pricing and Hedging he No-Negaive-Equiy Guaranee in Equiy Release Mechanisms, Journal of Risk and Insurance, 77: Liao, H.H., S.S. Yang and I.H. Huang(2007). The Design of Securiizaion for Longeviy Risk: Pricing under Sochasic Moraliy Model wih Tranche Technique. Presened a he Third Inernaional Longeviy Risk and Capial Marke Soluions Symposium, Taipei. 7. Wills, S, and M. Sherris(2010). Securiizaion, Srucuring and Pricing of Longeviy risk, Insurance: Mahemaics and Economics, 46 (1), Sherris, M. and S. Wills (2007). Financial innovaion and he hedging of longeviy risk. Asia Pacific Journal of Risk and Insurance 3(1), Zhai, David H.(2000), Reverse Morgage Securiizaions: Undersanding and Gauging he Risks, Special Repor, Moody s Invesors Service. 24

Developing Equity Release Markets: Risk Analysis for Reverse Mortgage and Home Reversion

Developing Equity Release Markets: Risk Analysis for Reverse Mortgage and Home Reversion Developing Equiy Release Markes: Risk Analysis for Reverse Morgage and Home Reversion Daniel Alai, Hua Chen, Daniel Cho, Kaja Hanewald, Michael Sherris Developing he Equiy Release Markes 8 h Inernaional

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Optimal Longevity Hedging Strategy for Insurance. Companies Considering Basis Risk. Draft Submission to Longevity 10 Conference

Optimal Longevity Hedging Strategy for Insurance. Companies Considering Basis Risk. Draft Submission to Longevity 10 Conference Opimal Longeviy Hedging Sraegy for Insurance Companies Considering Basis Risk Draf Submission o Longeviy 10 Conference Sharon S. Yang Professor, Deparmen of Finance, Naional Cenral Universiy, Taiwan. E-mail:

More information

Pricing and Securitization of Reverse Mortgage for Dependent Lives

Pricing and Securitization of Reverse Mortgage for Dependent Lives Pricing and Securitization of Reverse Mortgage for Dependent Lives Sharon S. Yang National Central University Corresponding Author: Sharon S. Yang, Associate Professor, Department of Finance, National

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

A General Pricing Framework for No-Negative-Equity. Guarantees with Equity-release Products: A Theoretical and

A General Pricing Framework for No-Negative-Equity. Guarantees with Equity-release Products: A Theoretical and A General Pricing Framework for No-Negaive-Equiy Guaranees wih Equiy-release Producs: A Theoreical and Empirical Sudy Jr-Wei Huang 1 Chuang-Chang Chang 2 Sharon S. Yang 3 ABSTRACT We invesigae sochasic

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

Risk Modelling of Collateralised Lending

Risk Modelling of Collateralised Lending Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

The Grantor Retained Annuity Trust (GRAT)

The Grantor Retained Annuity Trust (GRAT) WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business

More information

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did the Demand for Cash Decrease Recently in Korea? Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

More information

LIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b

LIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.

More information

MANAGING LONGEVITY RISKS IN THE FINANCIAL MARKETS: INNOVATE OR DIE

MANAGING LONGEVITY RISKS IN THE FINANCIAL MARKETS: INNOVATE OR DIE 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

More information

UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert

UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of Erlangen-Nuremberg Lange Gasse

More information

Equities: Positions and Portfolio Returns

Equities: Positions and Portfolio Returns Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment. . Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure

More information

Markit Excess Return Credit Indices Guide for price based indices

Markit Excess Return Credit Indices Guide for price based indices Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis

Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis Second Conference on The Mahemaics of Credi Risk, Princeon May 23-24, 2008 Credi Index Opions: he no-armageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo - Join work

More information

This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.

This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. This documen is downloaded from DR-NTU, Nanyang Technological Universiy Library, Singapore. Tile A Bayesian mulivariae risk-neural mehod for pricing reverse morgages Auhor(s) Kogure, Asuyuki; Li, Jackie;

More information

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios

More information

études et Dossiers No. 369 World Risk and Insurance Economics Congress 25-29 July 2010 Singapore Working Paper Series of The Geneva Association

études et Dossiers No. 369 World Risk and Insurance Economics Congress 25-29 July 2010 Singapore Working Paper Series of The Geneva Association Inernaional Associaion for he Sudy of Insurance Economics éudes e Dossiers éudes e Dossiers No. 369 World Risk and Insurance Economics Congress 25-29 July 2010 Singapore Working Paper Series of The Geneva

More information

SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES

SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES Man On Wong Essay on Welfare Effecs of Developing Reverse Morgage Marke in China Subjec SA0 Advisors Bing Zheng Chen James Orr Prepared a School of

More information

The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies

The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies 1 The Ineracion of Guaranees, Surplus Disribuion, and Asse Allocaion in Wih Profi Life Insurance Policies Alexander Kling * Insiu für Finanz- und Akuarwissenschafen, Helmholzsr. 22, 89081 Ulm, Germany

More information

Relationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith**

Relationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith** Relaionships beween Sock Prices and Accouning Informaion: A Review of he Residual Income and Ohlson Models Sco Pirie* and Malcolm Smih** * Inernaional Graduae School of Managemen, Universiy of Souh Ausralia

More information

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years.

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years. Currency swaps Wha is a swap? A swap is a conrac beween wo couner-paries who agree o exchange a sream of paymens over an agreed period of several years. Types of swap equiy swaps (or equiy-index-linked

More information

Analyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer s and the Policyholder s Perspective

Analyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer s and the Policyholder s Perspective Analyzing Surplus Appropriaion Schemes in Paricipaing Life Insurance from he Insurer s and he Policyholder s Perspecive Alexander Bohner, Nadine Gazer Working Paper Chair for Insurance Economics Friedrich-Alexander-Universiy

More information

Insurance Premium Structure of Reverse Mortgage Loans in Korea Seungryul Ma and Yongheng Deng. September, 2006

Insurance Premium Structure of Reverse Mortgage Loans in Korea Seungryul Ma and Yongheng Deng. September, 2006 Insurance Premium Srucure of Reverse Morgage Loans in Korea Seungryul Ma and Yongheng Deng Sepember, 2006 Absrac We analyze he insurance premium srucure of reverse morgage loans in Korea. Our analyses

More information

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions Developing Equiy Release Markes: Risk Analysis for Reverse Morgages and Home Reversions Daniel Alai 2, Hua Chen, Daniel Cho 2, Kaja Hanewald 2, and Michael Sherris 2 Absrac: Equiy release producs are sorely

More information

Option Put-Call Parity Relations When the Underlying Security Pays Dividends

Option Put-Call Parity Relations When the Underlying Security Pays Dividends Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,

More information

Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry

Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry IRES011-016 IRES Working Paper Series Breakeven Deerminaion of Loan Limis for Reverse Morgages under Informaion Asymmery Ming Pu Gang-Zhi Fan Yongheng Deng December, 01 Breakeven Deerminaion of Loan Limis

More information

Price elasticity of demand for crude oil: estimates for 23 countries

Price elasticity of demand for crude oil: estimates for 23 countries Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh

More information

I. Basic Concepts (Ch. 1-4)

I. Basic Concepts (Ch. 1-4) (Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing

More information

Extract from. Études et Dossiers No. 302. World Risk and Insurance Economics Congress. Inaugural Conference

Extract from. Études et Dossiers No. 302. World Risk and Insurance Economics Congress. Inaugural Conference Inernaional Associaion for he Sudy of Insurance Economics Éudes e Dossiers Exrac from Éudes e Dossiers No. 32 World Risk and Insurance Economics Congress Inaugural Conference 7 11 Augus 25 Sal Lake Ciy,

More information

Fifth Quantitative Impact Study of Solvency II (QIS 5) National guidance on valuation of technical provisions for German SLT health insurance

Fifth Quantitative Impact Study of Solvency II (QIS 5) National guidance on valuation of technical provisions for German SLT health insurance Fifh Quaniaive Impac Sudy of Solvency II (QIS 5) Naional guidance on valuaion of echnical provisions for German SLT healh insurance Conens 1 Inroducion... 2 2 Calculaion of bes-esimae provisions... 3 2.1

More information

LEASING VERSUSBUYING

LEASING VERSUSBUYING LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss

More information

Fair Valuation and Risk Assessment of Dynamic Hybrid Products in Life Insurance: A Portfolio Consideration

Fair Valuation and Risk Assessment of Dynamic Hybrid Products in Life Insurance: A Portfolio Consideration Fair Valuaion and Risk ssessmen of Dynamic Hybrid Producs in ife Insurance: Porfolio Consideraion lexander Bohner, Nadine Gazer Working Paper Deparmen of Insurance Economics and Risk Managemen Friedrich-lexander-Universiy

More information

Present Value Methodology

Present Value Methodology Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions Developing Equiy Release Markes: Risk Analysis for Reverse Morgages and Home Reversions Prepared by Daniel Alai, Hua Chen, Daniel Cho, Kaja Hanewald, and Michael Sherris Presened o he Acuaries Insiue Acuaries

More information

Measuring the Downside Risk of the Exchange-Traded Funds: Do the Volatility Estimators Matter?

Measuring the Downside Risk of the Exchange-Traded Funds: Do the Volatility Estimators Matter? Proceedings of he Firs European Academic Research Conference on Global Business, Economics, Finance and Social Sciences (EAR5Ialy Conference) ISBN: 978--6345-028-6 Milan-Ialy, June 30-July -2, 205, Paper

More information

ARCH 2013.1 Proceedings

ARCH 2013.1 Proceedings Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

More information

Chapter 9 Bond Prices and Yield

Chapter 9 Bond Prices and Yield Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

Optimal Investment and Consumption Decision of Family with Life Insurance

Optimal Investment and Consumption Decision of Family with Life Insurance Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker

More information

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,

More information

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying

More information

Financial Prequalification for a Contractor by using a Dynamic Threshold Cash Flow Based Model

Financial Prequalification for a Contractor by using a Dynamic Threshold Cash Flow Based Model Financial Prequalicaion for a Conracor by using a Dynamic Threshold Cash Flow Based Model Wen-Haw Huang, Hsien-Hsing Liao, Hui-Ping Tserng, and Shu-Yi Lee indusry, undersanding he variaion of cash flow

More information

On the Management of Life Insurance Company Risk by Strategic Choice of Product Mix, Investment Strategy and Surplus Appropriation Schemes

On the Management of Life Insurance Company Risk by Strategic Choice of Product Mix, Investment Strategy and Surplus Appropriation Schemes On he Managemen of Life Insurance Company Risk by raegic Choice of Produc Mix, Invesmen raegy and urplus Appropriaion chemes Alexander Bohner, Nadine Gazer, Peer Løche Jørgensen Working Paper Deparmen

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

INVESTMENT GUARANTEES IN UNIT-LINKED LIFE INSURANCE PRODUCTS: COMPARING COST AND PERFORMANCE

INVESTMENT GUARANTEES IN UNIT-LINKED LIFE INSURANCE PRODUCTS: COMPARING COST AND PERFORMANCE INVESMEN UARANEES IN UNI-LINKED LIFE INSURANCE PRODUCS: COMPARIN COS AND PERFORMANCE NADINE AZER HAO SCHMEISER WORKIN PAPERS ON RISK MANAEMEN AND INSURANCE NO. 4 EDIED BY HAO SCHMEISER CHAIR FOR RISK MANAEMEN

More information

Risk Management and Payout Design of Reverse Mortgages

Risk Management and Payout Design of Reverse Mortgages Risk Managemen and Payou Design of Reverse Morgages Daniel Cho, Kaja Hanewald and Michael Sherris School of Risk and Acuarial Sudies and Ausralian Research Council Cener of Excellence in Populaion Ageing

More information

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao, Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics 27 January 2008 Absrac We exend a reduced form model for

More information

The Interest Rate Risk of Mortgage Loan Portfolio of Banks

The Interest Rate Risk of Mortgage Loan Portfolio of Banks The Ineres Rae Risk of Morgage Loan Porfolio of Banks A Case Sudy of he Hong Kong Marke Jim Wong Hong Kong Moneary Auhoriy Paper presened a he Exper Forum on Advanced Techniques on Sress Tesing: Applicaions

More information

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees.

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees. The Impac of Surplus Disribuion on he Risk Exposure of Wih Profi Life Insurance Policies Including Ineres Rae Guaranees Alexander Kling 1 Insiu für Finanz- und Akuarwissenschafen, Helmholzsraße 22, 89081

More information

Annuity Decisions with Systematic Longevity Risk

Annuity Decisions with Systematic Longevity Risk Annuiy Decisions wih Sysemaic Longeviy Risk Ralph Sevens This draf: November, 2009 ABSTRACT In his paper we invesigae he effec of sysemaic longeviy risk, i.e., he risk arising from uncerain fuure survival

More information

An Optimal Strategy of Natural Hedging for. a General Portfolio of Insurance Companies

An Optimal Strategy of Natural Hedging for. a General Portfolio of Insurance Companies An Opimal Sraegy of Naural Hedging for a General Porfolio of Insurance Companies Hong-Chih Huang 1 Chou-Wen Wang 2 De-Chuan Hong 3 ABSTRACT Wih he improvemen of medical and hygienic echniques, life insurers

More information

Modeling a distribution of mortgage credit losses Petr Gapko 1, Martin Šmíd 2

Modeling a distribution of mortgage credit losses Petr Gapko 1, Martin Šmíd 2 Modeling a disribuion of morgage credi losses Per Gapko 1, Marin Šmíd 2 1 Inroducion Absrac. One of he bigges risks arising from financial operaions is he risk of counerpary defaul, commonly known as a

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk Jensen, Ninna Reitzel; Schomacker, Kristian Juul

A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk Jensen, Ninna Reitzel; Schomacker, Kristian Juul universiy of copenhagen Universiy of Copenhagen A Two-Accoun Life Insurance Model for Scenario-Based Valuaion Including Even Risk Jensen, Ninna Reizel; Schomacker, Krisian Juul Published in: Risks DOI:

More information

Stochastic Optimal Control Problem for Life Insurance

Stochastic Optimal Control Problem for Life Insurance Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian

More information

Dependent Interest and Transition Rates in Life Insurance

Dependent Interest and Transition Rates in Life Insurance Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies

More information

ECONOMIC AND BUSINESS REVIEW VOL. 13 No. 4 2011 251 272

ECONOMIC AND BUSINESS REVIEW VOL. 13 No. 4 2011 251 272 ECONOMIC AND BUSINESS REVIEW VOL. 13 No. 4 211 251 272 251 ADOPTION OF PROJECTED MORTALITY TABLE FOR THE SLOVENIAN MARKET USING THE POISSON LOG-BILINEAR MODEL TO TEST THE MINIMUM STANDARD FOR VALUING LIFE

More information

Chapter Four: Methodology

Chapter Four: Methodology Chaper Four: Mehodology 1 Assessmen of isk Managemen Sraegy Comparing Is Cos of isks 1.1 Inroducion If we wan o choose a appropriae risk managemen sraegy, no only we should idenify he influence ha risks

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual Health Insurance April 30, 2008 Pages 167-170 Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

More information

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees 1 The Impac of Surplus Disribuion on he Risk Exposure of Wih Profi Life Insurance Policies Including Ineres Rae Guaranees Alexander Kling Insiu für Finanz- und Akuarwissenschafen, Helmholzsraße 22, 89081

More information

Modeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling

Modeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se

More information

Chapter 1.6 Financial Management

Chapter 1.6 Financial Management Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1

More information

One dictionary: Native language - English/English - native language or English - English

One dictionary: Native language - English/English - native language or English - English Faculy of Social Sciences School of Business Corporae Finance Examinaion December 03 English Dae: Monday 09 December, 03 Time: 4 hours/ 9:00-3:00 Toal number of pages including he cover page: 5 Toal number

More information

A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates

A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates A comparison of he Lee-Carer model and AR-ARCH model for forecasing moraliy raes Rosella Giacomei a, Marida Berocchi b, Svelozar T. Rachev c, Frank J. Fabozzi d,e a Rosella Giacomei Deparmen of Mahemaics,

More information

1. Fund types and population covered

1. Fund types and population covered Performance and financial overview of invesmen funds - France 1 March 016 The Banque de France draws up he following informaion for invesmen funds: 1 monhly saisics on fund ousandings and flows, and on

More information

A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)

A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM) A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke

More information

Pricing Black-Scholes Options with Correlated Interest. Rate Risk and Credit Risk: An Extension

Pricing Black-Scholes Options with Correlated Interest. Rate Risk and Credit Risk: An Extension Pricing Black-choles Opions wih Correlaed Ineres Rae Risk and Credi Risk: An Exension zu-lang Liao a, and Hsing-Hua Huang b a irecor and Professor eparmen of inance Naional Universiy of Kaohsiung and Professor

More information

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry

More information

LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE:

LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE: LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE: 1. Inroducion and definiions 2. Insiuional Deails in Social Securiy 3. Social Securiy and Redisribuion 4. Jusificaion for Governmen

More information

Credit risk analysis of cash ow CDO structures

Credit risk analysis of cash ow CDO structures Credi risk analysis of cash ow CDO srucures Philippos Papadopoulos and Caroline I.M.L. Tan y November 30, 2007 Absrac Raing cash ow CDO srucures is a challenge. We develop a mehod ha o ers consisen and

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Cointegration Analysis of Exchange Rate in Foreign Exchange Market

Cointegration Analysis of Exchange Rate in Foreign Exchange Market Coinegraion Analysis of Exchange Rae in Foreign Exchange Marke Wang Jian, Wang Shu-li School of Economics, Wuhan Universiy of Technology, P.R.China, 430074 Absrac: This paper educed ha he series of exchange

More information

Payment Plans of Reverse Mortgage System in the Korean. Housing Market. Deokho Cho a, Seungryul Ma b,

Payment Plans of Reverse Mortgage System in the Korean. Housing Market. Deokho Cho a, Seungryul Ma b, 1 Paymen Plans of Reverse Morgage Sysem in he Korean Housing Marke Deokho Cho a, Seungryul Ma b, a Deparmen of Public Adminisraion, Daegu Universiy, Gyeongbuk, Souh Korea b Deparmen of Insurance and Finance,

More information

Longevity 11 Lyon 7-9 September 2015

Longevity 11 Lyon 7-9 September 2015 Longeviy 11 Lyon 7-9 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univ-lyon1.fr

More information

CALCULATION OF OMX TALLINN

CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, real-ime and closing value of he Index...3 3.2. Index

More information

Impact of Debt on Primary Deficit and GSDP Gap in Odisha: Empirical Evidences

Impact of Debt on Primary Deficit and GSDP Gap in Odisha: Empirical Evidences S.R. No. 002 10/2015/CEFT Impac of Deb on Primary Defici and GSDP Gap in Odisha: Empirical Evidences 1. Inroducion The excessive pressure of public expendiure over is revenue receip is financed hrough

More information

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion

More information

Rationales of Mortgage Insurance Premium Structures

Rationales of Mortgage Insurance Premium Structures JOURNAL OF REAL ESTATE RESEARCH Raionales of Morgage Insurance Premium Srucures Barry Dennis* Chionglong Kuo* Tyler T. Yang* Absrac. This sudy examines he raionales for he design of morgage insurance premium

More information

A Re-examination of the Joint Mortality Functions

A Re-examination of the Joint Mortality Functions Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali

More information

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world

More information

Contrarian insider trading and earnings management around seasoned equity offerings; SEOs

Contrarian insider trading and earnings management around seasoned equity offerings; SEOs Journal of Finance and Accounancy Conrarian insider rading and earnings managemen around seasoned equiy offerings; SEOs ABSTRACT Lorea Baryeh Towson Universiy This sudy aemps o resolve he differences in

More information

House Price Index (HPI)

House Price Index (HPI) House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales

More information

Tax Externalities of Equity Mutual Funds

Tax Externalities of Equity Mutual Funds Tax Exernaliies of Equiy Muual Funds Joel M. Dickson The Vanguard Group, Inc. John B. Shoven Sanford Universiy and NBER Clemens Sialm Sanford Universiy December 1999 Absrac: Invesors holding muual funds

More information

Loan-to-value ratio as a macroprudential tool Hong Kong SAR s experience and cross-country evidence

Loan-to-value ratio as a macroprudential tool Hong Kong SAR s experience and cross-country evidence Loan-o-value raio as a macroprudenial ool Hong Kong SAR s experience and cross-counry evidence Hong Kong Moneary Auhoriy I. Inroducion The 2008 09 global financial crisis has demonsraed ha moneary policy

More information

MULTI-PERIOD OPTIMIZATION MODEL FOR A HOUSEHOLD, AND OPTIMAL INSURANCE DESIGN

MULTI-PERIOD OPTIMIZATION MODEL FOR A HOUSEHOLD, AND OPTIMAL INSURANCE DESIGN Journal of he Operaions Research Sociey of Japan 27, Vol. 5, No. 4, 463-487 MULTI-PERIOD OPTIMIZATION MODEL FOR A HOUSEHOLD, AND OPTIMAL INSURANCE DESIGN Norio Hibiki Keio Universiy (Received Ocober 17,

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

THE IMPACT OF THE SECONDARY MARKET ON LIFE INSURERS SURRENDER PROFITS

THE IMPACT OF THE SECONDARY MARKET ON LIFE INSURERS SURRENDER PROFITS THE IPACT OF THE ECONDARY ARKET ON LIFE INURER URRENDER PROFIT Nadine Gazer, Gudrun Hoermann, Hao chmeiser Insiue of Insurance Economics, Universiy of. Gallen (wizerland), Email: nadine.gazer@unisg.ch,

More information

Forecasting Malaysian Gold Using. GARCH Model

Forecasting Malaysian Gold Using. GARCH Model Applied Mahemaical Sciences, Vol. 7, 2013, no. 58, 2879-2884 HIKARI Ld, www.m-hikari.com Forecasing Malaysian Gold Using GARCH Model Pung Yean Ping 1, Nor Hamizah Miswan 2 and Maizah Hura Ahmad 3 Deparmen

More information