Valuation of equity-indexed annuities under correlated jump–diffusion processes

Abstract

This article studies the problem of valuation of equity-indexed annuities (EIA) when the stock index follows a Hawkes jump–diffusion model to account for the jump risk and clustering of index price jumps. Further, the interest rate is assumed to be driven by Vasicek type model, correlated to the dynamics of the stock index. In the proposed framework, an analytical expression is obtained for the price of annual reset and point-to-point designs of EIAs by employing the measure change technique. The effects of the model parameters governing the jump risk and the clustering of jumps on the EIAs pricing are illustrated through numerical experiments.