The Guaranteed Minimum Withdrawal Benefits (GMWBs) are optional riders provided by insurance companies in variable annuities. They guarantee the policyholders' ability to get the initial investment back by making periodic withdrawals regardless of the impact of poor market performance. With GMWBs attached, variable annuities become more attractive. This type of guarantee can be challenging to price and hedge. We employ two approaches to price GMWBs. Under the constant static withdrawal assumption, the first approach is to decompose the GMWB and the variable annuity into an arithmetic average strike Asian call option and an annuity certain. The second approach is to treat the GMWB alone as a put option whose maturity and payoff are random. Hedging helps insurers specify and manage the risks of writing GMWBs, as well as find their fair prices. We propose semi-static hedging strategies that offer several advantages over dynamic hedging. The idea is to construct a portfolio of European options that replicate the conditional expected GMWB liability in a short time period, and update the portfolio after the options expire. This strategy requires fewer portfolio adjustments, and outperforms the dynamic strategy when there are random jumps in the underlying price. We also extend the semi-static hedging strategies to the Heston stochastic volatility model.

The Guaranteed Minimum Withdrawal Benefits (GMWBs) are optional riders provided by insurance companies in variable annuities. They guarantee the policyholders' ability to get the initial investment back by making periodic withdrawals regardless of the impact of poor market performance. With GMWBs attached, variable annuities become more attractive. This type of guarantee can be challenging to price and hedge. We employ two approaches to price GMWBs. Under the constant static withdrawal assumption, the first approach is to decompose the GMWB and the variable annuity into an arithmetic average strike Asian call option and an annuity certain. The second approach is to treat the GMWB alone as a put option whose maturity and payoff are random. Hedging helps insurers specify and manage the risks of writing GMWBs, as well as find their fair prices. We propose semi-static hedging strategies that offer several advantages over dynamic hedging. The idea is to construct a portfolio of European options that replicate the conditional expected GMWB liability in a short time period, and update the portfolio after the options expire. This strategy requires fewer portfolio adjustments, and outperforms the dynamic strategy when there are random jumps in the underlying price. We also extend the semi-static hedging strategies to the Heston stochastic volatility model.

A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase, and adverse interest rate experience at annuitization. The GMIB also provides an upside equity guarantee that resembles the benefit provided by a lookback option. We price the GMIB, and determine the fair fee rate that should be charged. Due to the long dated nature of the option, conventional hedging methods, such as delta hedging, will only be partially successful. Therefore, we are motivated to find alternative hedging methods which are practicable for long-dated options. First, we measure the effectiveness of static hedging strategies for the GMIB. Static hedging portfolios are constructed based on minimizing the Conditional Tail Expectation of the hedging loss distribution, or minimizing the mean squared hedging loss. Next, we measure the performance of semi-static hedging strategies for the GMIB. We present a practical method for testing semi-static strategies applied to long term options, which employs nested Monte Carlo simulations and standard optimization methods. The semi-static strategies involve periodically rebalancing the hedging portfolio at certain time intervals during the accumulation phase, such that, at the option maturity date, the hedging portfolio payoff is equal to or exceeds the option value, subject to an acceptable level of risk. While we focus on the GMIB as a case study, the methods we utilize are extendable to other types of long-dated options with similar features.

A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase, and adverse interest rate experience at annuitization. The GMIB also provides an upside equity guarantee that resembles the benefit provided by a lookback option. We price the GMIB, and determine the fair fee rate that should be charged. Due to the long dated nature of the option, conventional hedging methods, such as delta hedging, will only be partially successful. Therefore, we are motivated to find alternative hedging methods which are practicable for long-dated options. First, we measure the effectiveness of static hedging strategies for the GMIB. Static hedging portfolios are constructed based on minimizing the Conditional Tail Expectation of the hedging loss distribution, or minimizing the mean squared hedging loss. Next, we measure the performance of semi-static hedging strategies for the GMIB. We present a practical method for testing semi-static strategies applied to long term options, which employs nested Monte Carlo simulations and standard optimization methods. The semi-static strategies involve periodically rebalancing the hedging portfolio at certain time intervals during the accumulation phase, such that, at the option maturity date, the hedging portfolio payoff is equal to or exceeds the option value, subject to an acceptable level of risk. While we focus on the GMIB as a case study, the methods we utilize are extendable to other types of long-dated options with similar features.