Pricing Financial Options Embedded in Insurance Contracts

Variable Annuities represent a major part of the present annuity market, which has undergone enormous change in the last two to three decades. There are optional riders provided by insurance companies in variable annuities. Two main types of Variable Annuities’ guarantees can be distinguished: the guarantees in case of death (GMDB) and the guarantees in case of survival (GMAB, GMIB, GMWB and GLWB). The report is composed of three parts. First, each GMxB guarantee will be described with some of its variants. We introduce the fundamental assumptions of option theory and Black- Scholes and Merton model. We apply option theory to the embedded options of financial guarantees in insurance products. Later, we employ a special approach which is derived from Yan-Liu (2010) to price GMWBs. Under the constant static withdrawal assumption, the approach is to decompose the GMWB and the variable annuity into a call option and an annuity certain. We will present some basic results for each of GMWB and GMMB guarantees, illustrated by numerical examples. Once our main pricing framework is presented we will profit from it to study the impact of interest rate, market volatility, mortality and longevity risk. Overall, we claim that the proposed model provides further useful information about pricing insurance products with regard to existing economic conditions in Iran. Using this model, we are able to provide new innovative products which can be very critical and useful.