This thesis develops a contingent claim pricing model to compute the value of a popular insurance product on variable annuity called the Guaranteed Minimum Withdrawal Benefit (GMWB) under stochastic interest rates. This product promises to return the entire initial investment, with withdrawals periodically spread over the term of the contract, regardless of the market performance of the underlying asset portfolio. In our model, we assume that the policyholder withdraws a fixed amount during each period and holds the product to maturity. Under this assumption of static withdrawal, we show that the pricing problem under stochastic interest rates can be decomposed into pricing an Asian type put option plus a term-certain annuity. Since there is no simple closed form solution to price arith...[ Read more ]

This thesis develops a contingent claim pricing model to compute the value of a popular insurance product on variable annuity called the Guaranteed Minimum Withdrawal Benefit (GMWB) under stochastic interest rates. This product promises to return the entire initial investment, with withdrawals periodically spread over the term of the contract, regardless of the market performance of the underlying asset portfolio. In our model, we assume that the policyholder withdraws a fixed amount during each period and holds the product to maturity. Under this assumption of static withdrawal, we show that the pricing problem under stochastic interest rates can be decomposed into pricing an Asian type put option plus a term-certain annuity. Since there is no simple closed form solution to price arithmetic Asian options, we develop tight lower and upper bounds to approximate the price of this Asian type option. Numerical experiments show that we can obtain very accurate bounds in spite of the long maturities and high volatilities. Finally, the pricing behaviors of the GMWB to different model parameters are presented.