Pricing Ratchet Equity-Indexed Annuities with Early Surrender Risk in a CIR++ Model

Abstract

In this article we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique that permits us to obtain a first-order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without a global minimum contract value. Numerical comparisons show the reliability of the proposed methods.

Acknowledgments

This research was supported by MIUR (Prin 2007), NSFC (No. 10801139), and the MOE Project of the Key Research Institute of Humanities and Social Sciences at Universities (No. 11JJD790053, No. 12JJD790017). We are indebted to Prof. Sheldon Lin for suggesting to us the cancellation fee in the surrender case. We also thank the referees for their valuable comments and suggestions.