HEDGING LONGEVITY RISK: CAPITAL MARKET SOLUTIONS

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1 UNIVERSITÉ PARIS-DAUPHINE Séminaire Ageing and Risk HEDGING LONGEVITY RISK: CAPITAL MARKET SOLUTIONS JORGE MIGUEL BRAVO University of Évora, Department of Economics Évora Portugal, Paris, November 20, 2007 Jorge Miguel Bravo (2007) 1

2 Agenda 1. Demographic trends: The Portuguese experience 2. Financial implications of longevity risk 3. The nature of mortality and longevity risks 4. Projecting mortality trends 5. Approaches in managing longevity risk 6. Portfolio diversification 7. Risk transfer solutions Product design, buyout of the liabilities Reinsurance markets Securitization Capital market solutions: Longevity/survivor bonds, Mortalityderivatives, Jorge Miguel Bravo (2007) 2

3 Demographic trends: life expectancy Graph of x e x for men (left) and women (right) ex ex Age Age Jorge Miguel Bravo (2007) 3

4 Demographic trends: mortality rates (q x ) Graph of x ln q for men (left) and women (right) x log(qx) log(qx) Age Age Declining mortality rates at all ages hump in mortality around ages Jorge Miguel Bravo (2007) 4

5 Demographic trends: rectangularization x l / l Graph of for men (left) and women (right): the x 0 survival function becomes more and more rectangular lx/l lx/l Age Age Jorge Miguel Bravo (2007) 5

6 Demographic trends: fertility Fertility rate: Growth EU Italy France ,83 Spain UK Portugal Source: Eurostat Dependency Ratios the Young (0-19 over 20-59) Growth Growth EU % -36.7% France % -29.0% UK % -29.1% Portugal % -43.2% Source: Eurostat Jorge Miguel Bravo (2007) 6

7 Demographic trends: dependency ratios Dependency Ratios the Elderly (60 & + over 20-59) Growth Growth EU % 74.2% France % 54.3% UK % 45.9% Portugal % 103.2% Source: Eurostat Ageing Index EU France UK Portugal Source: Eurostat Jorge Miguel Bravo (2007) 7

8 Demographic trends: financial implications Traditional public pay-as-you-go social security systems become unsustainable Market trend away from defined-benefit corporate pension systems towards defined-contribution schemes The extended mobility of the workforce has broken down traditional family networks Labour market uncertainty, housing bubble Consequences: Individuals will have to become more self-reliant and will want to change their sources of income in retirement Insurance companies have an important role but will have to address the problem of pricing and hedging for longevity risks Jorge Miguel Bravo (2007) 8

9 Mortality risk and Longevity risk Projected (solid line) vs experienced (dots) mortality rates for a given age x q () x t q () x t q () x t q () x t q () x t q () x t ( A) time ( B) time ( C) time Case (A): random fluctuations around expected values Case (B): random fluctuations around and random deviations from expected values Case (C): random fluctuations and catastrophe mortality Jorge Miguel Bravo (2007) 9

10 Mortality risk and Longevity risk Case (A) Process risk Pooling risk (large, homogeneous portfolios) Hedging through enforcement of pooling effects Case (C) Systematic risk (but higher mortality than expected) Case (B) Experienced trend different from expected one systematic risk, traditional hedging tools do not apply Longevity risk: the risk that individuals will systematically live longer than expected Mortality risk: the risk that individuals will live shorter than expected (i.e., their mortality is higher than expected) Jorge Miguel Bravo (2007) 10

11 Mortality risk and Longevity risk Mortality trends require the adoption of projected lifetables when living benefits are dealt with Whatever projection model is adopted, the future mortality is random systematic deviations may occur Deviations from expected values are explained by: the stochastic nature of mortality process risk the calculation of expected mortality rates is based on the choice of a projection model model risk the estimation of the parameters of the projection model parameter risk A useful framework is given by stochastic mortality models Jorge Miguel Bravo (2007) 11

12 Projecting mortality trends Approaches in constructing prospective lifetables: Vertical Horizontal Diagonal Projection Methods: Parametric models: see e.g., Benjamin & Soliman (1993), Sithole et al. (2000), Pittaco(2004) Lee-Carter methodology: see e.g., Lee & Carter (1992), Lee (2000), Tuljapurkar et al. (2000)), Wong-Fupuy & Haberman (2004), Bravo (2007), Poisson log-bilinear methodology: see e.g., Brouhns et al. (2002a), Renshaw e Haberman (2003a,b), Bravo (2007), Projection with reference to optimal and/or model lifetables Jorge Miguel Bravo (2007) 12

13 Hedging longevity risk Hedging perspective: Individual protection (insured, annuitant, ) Global risk management (pension plan sponsors, life insurance companies, annuity providers, government, ) Approaches in managing longevity risk 1. Hedge the risk while retaining it Portfolio diversification 2. reduce the risk by transferring it to another counterpart Product design, buyout of the liabilities Reinsurance markets Securitization Capital market solutions: Longevity/survivor bonds, Mortality-derivatives, Jorge Miguel Bravo (2007) 13

14 Longevity risk: individual protection The private sector (insurance industry) is well placed to aid retirees in addressing their financial needs, both in their asset accumulation and decumulation phases In the accumulation phase By helping individuals build up a desired level of savings throughout their working years: in a flexible way (in the amount and timing of their contributions to the capitalisation plan) in an efficient way (via investment diversification, gradual adjustment of the risk/return profile based on age, tax advantages, ) In the decumulation phase By allowing individuals to run their asset pool smoothly while offering protection against longevity/inflation: various types of annuities health care and long-term car insurance wealth monetisation (e.g., reverse mortgages) wealth transfer in case of early death Jorge Miguel Bravo (2007) 14

15 Distinguished features of annuity products Protection against longevity risk Embedded guarantees Inflation-linked payouts Equity market-linked payouts Mortality-linked payouts (with-profit or participating annuities) Additional guarantees: minimum investment return, minimum death benefit, minimum accumulation benefit, minimum withdrawal/income benefit, number of people covered, health-care protection, Tax advantages Jorge Miguel Bravo (2007) 15

16 Annuity markets constraints Demand constraints Annuities are perceived as expensive Seen only as a financial investment in the accumulation phase Insufficient tax incentives Bequest and liquidity motives Supply constraints Adverse selection problems Pricing problems: lack of prospective lifetables Lack of solutions to manage longevity risk Regulation Jorge Miguel Bravo (2007) 16

17 Hedging longevity risk: diversification Explore natural hedging opportunities combining portfolios with complimentary cash flows (e.g., assurances and annuities) Long vs short exposure Annuities, DB pension plans short longevity or, equivalently, long mortality Life insurance portfolio long longevity or, equivalently, short mortality International diversification mortality shifts observed in different countries are not perfectly correlated Mortality shifts affect different socioeconomic groups differently Diversification enhancement through swap agreements Jorge Miguel Bravo (2007) 17

18 Risk transfer mechanisms: product design Increase safety loadings Write annuities with premiums indexed to the evolution of longevity Replace traditional non-participating annuities with participating (with-profit) contracts that pass part of the exposure to longevity risk to surviving participating policyholders should offer additional return to compensate for longevity risk Implement pricing strategies that differentiate among individuals according to their specific risk factors (e.g., smoking) contingency loadings Alternative: Buyout (i.e., externalization) of the pension plan Jorge Miguel Bravo (2007) 18

19 Capital market solutions: Longevity Bonds General structure: Classical bond whose coupons and/or principal are linked to the evolution of mortality (survivor index) in a given reference population Types of Longevity Bonds (LBs) Longevity Zeros (LZs): similar to zero coupon bonds Survivor bonds: continue to make payments for as long as any member of the population is still alive Principal-at-risk LBs: fixed or interest rate sensitive coupons, but whose principal is contingent upon the evolution of a survivor index Inverse LBs: comparable with conventional floaters Deferred longevity bonds Mortality Catastrophe Bond Jorge Miguel Bravo (2007) 19

20 The EIB/BNP Longevity Bond Announced by the EIB in November 2004; Structurer BNP Initial value of 540m, initial coupon of 50m, maturity 25 years Payments directly proportional to the evolution of survivor index (England and Wales male population aged 65 in 2002) f ( S ) 50m S, t 1, 2,..., T 25 t t t Features: Bond designed to be a hedge to the holder The issuer gains (loses) if S t is lower (higher) than expected The bond is a hedge against a portfolio dominated by annuities Designed to protect against longevity risk Supplemented by a cross-currency (fixed-sterling-for-floatingeuro) interest-rate swap Jorge Miguel Bravo (2007) 20

21 The Swiss Re mortality catastrophe bond Maturity: 3 years; principal $400m, floating coupon of LIBOR+135 basis points; Issued in December 2003, through a SPV called Vita Capital Principal repayment dependent on the realized value of a weighted index of mortality rates in 5 countries, M t Designed to be a hedge to the issuer Payment schedules LIBOR spread t 1,..., T 1 ft() LIBOR spread max{ 0, 100% Lt } t T t 0% Mt 13. M0 L [( M 13. M ) /( 02. M )] 100% if 13. M M 15. M 100% 1. 5M0 Mt t t t 0 Jorge Miguel Bravo (2007) 21

22 Longevity bonds: complications (1) Imbalance in the market: natural excess of demand Potential issuers: private companies with a natural long exposure to longevity risk (e.g., pharmaceuticals, residential car homes, housing associations, biotech companies) Government issuance of LBs (pros and cons) In order to suppress a market failure (lender of last resort) By spreading the risk over a huge amount of taxpayers this will eliminate the market price of risk States contribute to the increase in longevity allows a more efficient intergenerational risk sharing The state is already highly exposed to longevity risk through DB pension systems The state diversifies only within the taxpayers group Jorge Miguel Bravo (2007) 22

23 Longevity bonds: complications (2) Survivor Index problems Indexes are constructed from data published infrequently and subject to incurred-but-not-reported errors The historical data typically needs to smoothed method risk Indexes are subject to integrity and contamination risk Issues of moral hazard: data providers have much earlier access to data than investors Survivor indexes involve projections of future mortality that are subject to both model and parameter risk Jorge Miguel Bravo (2007) 23

24 Longevity bonds: complications (3) Valuation We cannot use standard non arbitrage arguments to price longevity securities because of market incompleteness Modelling issues: representation of mortality uncertainty Estimation issues: in particular, market price of longevity risk Alternative approaches Risk-neutral approach Use classic premium principles (e.g., standard deviation principle) Distortion approaches (Wang transform) Sharpe ratio Consumption CAPM Mean-variance and Risk minimization strategies Jorge Miguel Bravo (2007) 24

25 Standard deviation premium principle Consider the classic standard deviation premium principle P P HX [ ] E( x) Var( x), >0 We assume that the force of mortality is represented by and stochastic differential equation d () t a( ()) t dt () t dw(), t () 0 x x x x x Denoting the survival probability by an affine function where p ( t) exp AxtT (,, ) BxtT (,, ) ( t) T t x t x t 2 2 B () ab() B () 1, B() 0 0 A () 2a B(), A() 0 0 Jorge Miguel Bravo (2007) 25

26 Mortality-derivatives Mortality Swaps Example: vanilla mortality swap Analogous to an interest rate swap (IRS) Agreement between two counterparties to exchange preset payments that decline over time in line with the survivor index anticipated at time 0 (fixed leg), for payments dependent on the realised value of the survivor index at time t (floating leg) Mortality Futures Underlying asset (process): Longevity Bonds, annuities, survivor index Delivery dates Critical issues: need for a large, active, liquid spot market for the underlying Jorge Miguel Bravo (2007) 26

27 Mortality-derivatives Mortality Options Useful for hedger who want to protect their downward exposure, but leave upside potential Speculators who wish to trade views on the volatility of mortality rates rather than on the levels The valuation and risk management of options requires a good stochastic mortality model d () t a () t dt () t dw() t dj(), t () 0 x x x x x Possible types of options Survivor caps and floors Annuity futures options Mortality swaptions Jorge Miguel Bravo (2007) 27

28 Stochastic mortality model Example: affine-jump diffusion model (Feller with jumps) d () t a () t dt () t dw() t dj(), t () 0 x x x x x J(t) is a compound Poisson process with constant jump intensity and jump-sizes following and asymmetric doubly-exponential distribution Denoting the survival probability by an affine function p ( t) exp AxtT (,, ) BxtT (,, ) ( t) T t x t x t Feynman-Kac representation B () ab() B () x t() t A () 2 where B () ab() B (), B() A () 0, A() Jorge Miguel Bravo (2007) 28

29 Stochastic mortality model Closed-form solution for the survival probability: p ( t) exp AxtT (,, ) BxtT (,, ) ( t) T t x t x t 1 e B(), e a 2 ( a ) 0 2 ( a) 1 2 A() 0 Jorge Miguel Bravo (2007) 29

30 Stochastic mortality model: calibration S(x) y1970 Feller c/ saltos S(x) y1970 Feller c/ saltos Idade Idade S(x) y2004 Feller c/ saltos S(x) y2004 Feller c/ saltos Idade Idade Jorge Miguel Bravo (2007) 30

31 Risk transfer mechanisms: reinsurance Reinsurance arrangements can be conceived, at least in principle (1) Surplus reinsurance: high amount annuities are ceded (2) Excess of Loss reinsurance: the reinsurer pays the final part of the annuity while exceeding a given term (age 85) (3) Stop-Loss reinsurance on assets: the reinsurer partially covers the required portfolio reserve (4) Stop-Loss reinsurance on cash flows: the reinsurer intervenes when the annual amount of benefits to be currently paid is above a given threshold Arrangement (1): coverage of process risk (2), (3), (4): designed to face longevity risk (2): intervention on an individual level (3), (4): intervention at the portfolio level Jorge Miguel Bravo (2007) 31

32 XL Reinsurance (XL) Feature: the reinsurer pays to the cedant the final part of the annuity if the annuitant outlives a given age (e.g., 85) For the annuity provider, whole life annuities are converted into temporary life annuities (the reinsurer takes on a deferred whole life annuity) annuitants reinsurer's intervention lifetime Jorge Miguel Bravo (2007) 32

33 Stop-Loss reinsurance on assets (SLA) General aspects arrangement defined on a short-medium period basis reinsurer s intervention aim at preventing the insolvency of the cedant, caused by mortality deviation Rationale The effect of mortality deviations is perceived comparing portfolio assets at a given time with the portfolio reserve required to meet the insurer s obligations Loss to the annuity provider: lack of assets The reinsurer covers partially/totally this lack Reinsurer s intervention occur only at the given times (end of each reinsurance period) Jorge Miguel Bravo (2007) 33

34 Stop-Loss reinsurance on assets (SLA) Assets and reserve assets available reinsurer's intervention required portfolio reserve time Further aspects Choice of the reinsurance period: too short emphasize random deviation effects; too long severity of longevity risk to the reinsurer Assets to be referred to must be carefully defined Pricing: premium paid at the beginning of the reinsurance period Jorge Miguel Bravo (2007) 34

35 Stop-Loss reinsurance on cash flows Quantity referred to: annual outflows of the annuity provider Rationale: at a given point in time longevity risk is perceived if the amount of benefits to be currently paid to annuitants is higher than expected Arrangement: at given times (e.g., every year) the reinsurer takes charge of a part of such extra-amount Only longevity risk should be involved take a first step surplus reinsurance and/or set a trigger level for the reinsurer s intervention higher than the expected value of the amount of benefits Stop-loss upper limits for the amount to be paid by the reinsurer Jorge Miguel Bravo (2007) 35

36 Comparing the three arrangements XL arrangement very good for the cedant very risky for the reinsurer Stop-Loss arrangement on assets Involvement of the cedant for the whole life of the cohort Disadvantage for the cedant: losses within the reinsurance period (i.e., previous to its end) are nor involved Disadvantage for the reinsurer: possible lack of control on the management of cedant s assets Stop-Loss arrangement on cash flows Involvement of the cedant for the whole life of the cohort Reinsured quantities easy to measure Possibility to combine with securitization strategies Jorge Miguel Bravo (2007) 36

37 THANK YOU JORGE MIGUEL BRAVO University of Évora, Department of Economics Évora Portugal, Jorge Miguel Bravo (2007) 37

Pricing death. or Modelling the Mortality Term Structure. Andrew Cairns Heriot-Watt University, Edinburgh. Joint work with David Blake & Kevin Dowd

Pricing death. or Modelling the Mortality Term Structure. Andrew Cairns Heriot-Watt University, Edinburgh. Joint work with David Blake & Kevin Dowd 1 Pricing death or Modelling the Mortality Term Structure Andrew Cairns Heriot-Watt University, Edinburgh Joint work with David Blake & Kevin Dowd 2 Background Life insurers and pension funds exposed to