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

Abstract

In connection with a problem posed by Kijima and Wong [11], 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 which permits to obtain a first order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without global minimum contract value. Numerical comparisons show the reliability of the proposed methods. Key-words:

American options and stochastic interest rates

“…positive) correlation between the bond and the equity prices 2 . The literature on American equity options 3 has so far focused on alternative stochastic interest rates models, such as the CIR one, based on the seminal work of Cox et al (1885) (see Medvedev and Scaillet (2010), Boyarchenko and Levendorskiǐ (2013) and Wei et al (2013), among others). Our paper is, to our knowledge, the first that addresses the valuation of American equity options in a stochastic interest rate framework of Vasicek type, allowing for the possibility of negative interest rates.…”

Fair evaluation of life insurance policies with periodic rebalancing between asset portfolios and interest rate guarantee

“…For these reasons, lattice-based models have been extensively applied in life insurance to solve the evaluation problem relative to policies with complex embedded riders. Among others, we may cite Bacinello [1] who considered guaranteed participating contracts with embedded surrender options, Yang and Dai [8] who proposed a model to evaluate variable annuities with a guaranteed minimum withdrawal benefit, and Wei et al [9] who considered the problem of evaluating ratchet equity-indexed annuities under stochastic interest rates. In the present paper, the problem of evaluating at fair rates the policy above described has been tackled in the Cox-Ross-Rubinstein (CRR hereafter [4]) framework.…”