Valuation of Guaranteed Annuity Options

Abstract

This paper analyzes the problem of guaranteed annuity options (GAOs) attached to pension policies issued by life insurance companies in Britain. GAOs offer policyholders the right to convert the sum assured at normal retirement age into a life annuity at the better market rate (MAR) prevailing at the time of conversion and a guaranteed rate (GAR). The insurer provides the interest-rate options for the policyholder. In this paper, we attempt to value the GAO and extend the existing literature by considering surrender in pricing GAO. The valuation framework is built on the one-factor Cox-Ingersoll-Ross framework. We make use of the Least Squares Monte Carlo approach proposed by Longstaff and Schwartz (2001) to model policyholders' surrender behaviors. Our results show that the insurer might overestimate the price of GAO when ignoring the surrender behaviors. In addition, the option values are very sensitive to guaranteed annuity rates, long-term mean of interest rates, diffusion factors of interest-rate models, correlation coefficient between equity fund values and interest rates, and diffusion factors of equity fund value.