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SECURITIZATION OF MORTALITY RISKS IN LIFE ANNUITIES

SECURITIZATION OF MORTALITY RISKS IN LIFE ANNUITIES. YIJIA LIN AND SAMUEL H. COX Доклад подготовила студентка 61УРАМ Ящук М. Individual Annuity Market in the United States. Bab y boom

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SECURITIZATION OF MORTALITY RISKS IN LIFE ANNUITIES

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  1. SECURITIZATION OF MORTALITY RISKS IN LIFEANNUITIES YIJIA LIN AND SAMUEL H. COX Доклад подготовила студентка 61УРАМ Ящук М.

  2. Individual Annuity Market in the United States • Baby boom the baby boom cohort in the USA nears and moves into retirement => increased attention to issues of old-age income security • Social Security Reform

  3. Demand for Mortality Based Securities • There is some relation between mortality securities and equity market returns • But investors may buy mortality based bonds as a diversification, even if mortality risk has a positive or negative correlation with the market.

  4. Supply of Mortality Based Securities • Hedging longevityrisk • (in comparison with reinsurance) • lower costs in the long run • more favorable contracts • elimination of default risk • Raising Required Capital

  5. Securitization vs. reinsurance

  6. Difficulties in Accurate Mortality Projection • Different Opinions in Mortality Trend. • Technical Difficulties in Mortality Projections • Quality of Data • Projection Models

  7. Mortality Swaps (1) • 1,000 per year per annuitant • the number of survivors to year t =1000 • The insurer and its swap counterparty agree on a level • In year t the insurer pays a fixed amount 1000to the counterparty and receives 1000

  8. Mortality Swaps (2) The value of the cash flow to the insurer for an n–year swap is • Where denotes the expected number of survivors among the N initial annuitants and is the discount factor based on the current bond market prices. • If the counterparties agree to =then V = 0 and no initial exchange of cash is required to initiate the swap

  9. Wang‘smethodofpricingrisks (1) • Let Φ(x) be the standard normal cumulative distribution function with a probability density function Distortion operator for 0<u<1 Consider an insurer’s liability X over a time horizon [0,T]

  10. Wang‘smethodofpricingrisks (2) • The value or fair price of the liability is the discounted expected value under the distribution obtained from the distortion operator • The formula for price: where )= . The parameter is called the market price of risk, reflecting the level of systematic risk.

  11. Market price of risk λ • Adapted to survival model, the transform is • is from 1995 US Buck Annuity Mortality Tables, for males and females separately • commission rate = 4%

  12. Mortality Bond Structure (1) • Nannuitants, all age x = 65 at the time the bond is issued • The corresponding strikelevel for each age will be • The number of survivors is the number of lives attaining age in the survivorship group set in the contract • The coupons are risky, but the principal is always paid at maturity

  13. Mortality Bond Structure (2) The bondholder’s payment at the end of year t is for t=1,2…,T T- the term of the mortality bond (30 years when the bond is issued)

  14. Mortality Bond Structure (3) • The survivalprobability • The distribution of the number of survivors has a binomial distribution with number of trials N and success probability • N is rather large, we can use the normal approximation with parameters and

  15. Mortality Bond Structure (4) The expected value of the bondholder’s coupon: Where Φ(z) denotes the standard normal cumulative density

  16. Mortality Bond Structure (5) • The bondholders are more likely to get the coupons in the earlier years than in the later years • The price of the mortality bond will be • where d(0,t) is the discount factor based on the risk free interest rate term structure at the time the bond is issued • F – the face amount

  17. Insurer’smortalitybondhedge • The insurer sells k bonds • At the same time the insurer buys k straight bonds with the same coupon rate as the annuity-based bonds

  18. Conclusions (1) • There is a growing demand for a long term hedge against improving annuity mortality • There is a trend of privatizing social securities systems with insurers taking more longevity risk • Insurers will need increased capacity to take on longevity risk and securities markets can provide it

  19. Conclusions (2) • Compared with the reinsurance market, securitization of mortality risks has • longer duration • higher capacity • possibly lower cost • It can help solve the difficulties in managing annuity mortality risk.

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