Equity-linked products: evaluation of the dynamic hedging errors under stochastic mortality

Abstract

In this paper, we analyze the effect of unpredicted changes in mortality rates on the risk incurred by the sale of equity-indexed annuities (EIAs). Jumps in mortality indices due to catastrophes (for example, the 1918 flu pandemic) may occur in the future, causing important financial losses to insurers selling products offering death benefits. Thus, we analyze the distribution of hedging errors extracted from the dynamic hedging strategy underlying the fair valuation. To model mortality jumps stochastically, we use a regime-switching model introduced by Milidonis et al. (North Am Actuarial J 15(2):266–289, 2011). We then employ Esscher transforms to obtain closed-form expressions for the price of a term-end EIA at any time between the inception of the contract and its maturity date. The hedging strategy is derived from that valuation, and hedging errors are extracted from this strategy since it is not self-financing. A detailed numerical analysis is performed for a term-end EIA.