The fair valuation problem of guaranteed annuity options:

The stochastic mortality environment case

Laura Ballotta ,Steven Haberman

• 1. introduction• 2. A valuation approach for guaranteed annuity

options• 3. A stochastic approach to mortality risk: the

basic model and its extensions• 4. A model for the financial risk and the GAO

valuation formula• 5. Numerical calculations and sensitivity analysis

Guaranteed annuity option

• Guaranteed annuity option(GAO) is a contract giving the holder the right to receive at retirement the greater of

(a) a cash payment equal to the current value of the investment in the equity fund, S, (b)the expected present value of the life annuity obtained by converting this investment at the guaranteed rate.

• Assumption:1. The mortality risk is independent of the financial

risk.2. Single premium S0(ignore any expense)3. The market is frictionless and competitive market

with continuous trading• Model1. Heath-Jarrow-Morton for interest rate2.Bullotta and Haberman for mortality intensity

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