Valuation of a Guaranteed Minimum Income Benefit

Abstract

With a deferred variable annuity the policyholder pays an upfront premium to the insurance company, which is then invested in the financial markets for many years (the accumulation phase) until the policyholder decides to convert their investment (often at retirement age) into a stream of variable annuity payments. A Guaranteed Minimum Income Benefit (GMIB) is an option that may be included at inception of a variable annuity contract that, in exchange for small fees charged by the insurer, gives the policyholder a right to receive a guaranteed minimum level of annuity payments upon annuitization. A GMIB is an attractive option because it protects the policyholder’s investment against poor market performance during the accumulation phase. The value of a GMIB is affected by investment account returns, interest rates, and mortality. The intention of this paper is to value a GMIB in a complete market, focusing on the sensitivity of the GMIB value to the financial variables. Mortality is not incorporated into the valuation. We present a comprehensive sensitivity analysis of the model employed. We decompose a GMIB payoff, which is rather complicated, to analyze what drives the value of a GMIB. Our approach offers a simple but effective way for insurers to measure the value of the GMIBs they offer, and it provides insights into the risk management of GMIBs and other guarantees that provide similar payoffs. Our model suggests that the fee rates charged by insurance companies for the GMIB option may be too low.