Financial Economic Valuation of Guaranteed Minimum Withdrawal Bene\u85ts in Variable Annuities

Anna Abaimova for helpful research assistance. We use No Arbitrage techniques to value an insurance feature available on many variable annuity (VA) policies called a Guaranteed Minimum Withdrawal Bene\u85t (GMWB). The GMWB is portfolio insurance on an internal rate of return, as opposed to a guaranteed point-to-point investment rate of return. They are typically sold to retail investors, can not be easily traded in the secondary market and have penalties associated with early surrender. Like all VA policies and in contrast to standard exchange traded options insurance companies charge for this protection by deducting an ongoing fraction of assets, as opposed to an up-front fee. Given all these non standard elements, we provide two extreme approaches to analyzing, valuing and managing the risk a GMWB. First, we take a static actuarial approach that assumes individual investors behave passively in utilizing the guarantee. In this case we show the product can be decomposed into a Quanto Asian Put plus a generic term-certain annuity. The opposite assumption is that investors are dynamically rational and seek to maximiz