Pricing Equity‐Indexed Annuities under Stochastic Interest Rates Using Copulas

Abstract

We develop a consistent evaluation approach for equity‐linked insurance products under stochastic interest rates. This pricing approach requires that the premium information of standard insurance products is given exogenously. In order to evaluate equity‐linked products, we derive three martingale probability measures that reproduce the information from standard insurance products, interest rates, and equity index. These risk adjusted martingale probability measures are determined using copula theory and evolve with the stochastic interest rate process. A detailed numerical analysis is performed for existing equity‐indexed annuities in the North American market.