Pricing Equity-Indexed Annuities with Surrender Options in a Stochastic Interest Rates Environment

Abstract

The aim of this paper is to value EIA contracts with surrender option at a fair price in a stochastic interest rate environment. A non Gaussian model is proposed where a new process called Kou Regime Switching process is introduced to give a more realistic modelling for financial prices. A general methodology is proposed and applied to mix GMDB and GMMB contract. Quasi-closed form solutions are given when the surrender clause is not present and this solution is incorporated into a LSMC algorithm to solve the pricing problem in the surrender case.

Keywords: equity indexed-annuities, variable annuities, surrender options, regime switching models, jump diffusion, stochastic interest-rate models, fast Fourier transform