Pricing guaranteed minimum withdrawal benefits under stochastic interest rates
研究了在Vasicek随机利率框架下，带有最低提取利益保证（GMWB）的可变年金的定价问题，推导了公平价值的解析近似解，并给出了价格函数的上下界。
We consider the pricing of variable annuities with the Guaranteed Minimum Withdrawal Benefit (GMWB) under the Vasicek stochastic interest rate framework. The holder of the variable annuity contract pays an initial purchase payment to the insurance company, which is then invested in a portfolio of risky assets. Under the GMWB, the holder can withdraw a specified amount periodically over the term of the contract such that the return of the entire initial investment is guaranteed, regardless of the market performance of the underlying asset portfolio. The investors have the equity participation in the reference investment portfolio with protection on the downside risk. The guarantee is financed by paying annual proportional fees. Under the assumption of deterministic withdrawal rates, we develop the pricing formulation of the value function of a variable annuity with the GMWB. In particular, we derive the analytic approximation solutions to the fair value of the GMWB under both equity and interest rate risks, obtaining both the lower and upper bounds on the price functions. The pricing behavior of the embedded GMWB under various model parameter values is also examined.