Fourier-Cosine Method for Pricing Equity-Indexed Annuity under Heston Model

Abstract

In this paper, a pricing method based on the Fourier-Cosine series expansion is introduced for pricing equity-indexed annuities (EIAs) under the Heston model. By means of the Fourier-Cosine series expansion, the density function of the underlying indexed is recovered from its characteristic function, and then yields an efficient way for EIAs pricing. To show the accuracy of the Fourier-Cosine expansion method, numerical experiments, we provide the numerical results of EIAs price for the classical Black-Scholes model. It is shown that the computation results obtained by the Foueier-Cosine series are as accurate as those obtained by using the Monte Carlo simulation method. The Fourier-Cosine expansion method can be used to obtain the break-even participation rate under the Heston model with or without a cap in simple ratchet EIAs.