A dimension-reduction algorithm for the valuation of surrender options in EIA contracts with stochastic interest rates

Abstract

This paper proposes a fast algorithm for the fair valuation of a ratchet-type equity-indexed annuity (EIA) endowment contract with surrender options under Vasicek stochastic interest rate models. Traditionally, the valuation for the indexed equity and interest rate of an American-type surrender option is performed under two-dimensional tree models, which is time-consuming for computation. This paper first applies the Black–Scholes method for ratchet-type options to reduce the two-dimensional tree structure to single one. Next, to overcome the path dependent problem inherent in the ratchet option, we also propose a recursive formula to implement the backward computation. By using the proposed algorithm, we are able to perform numerical analysis to verify that surrender options are more valuable with the increase of interest rates. High interest rate volatility enhances both the bonus and surrender option values entitled to the policyholder. A numerical experiment also shows that increasing interest rates may decrease the bonus option value but increase the surrender option value. These results can provide suggestions for insurance companies regarding the issue of EIA policies.