Pricing Equity-indexed Annuities When Discrete Dividends Follow a Markov-Modulated Jump Diffusion Model

Abstract

The Equity-Indexed annuities (EIAs) provide investors not only a minimum rate of return but also an opportunity to gain a potential profit that is linked to the performance of an equity index, typically SP 500. These properties make EIAs become very popular in the market and receive considerable attention in the actuarial literature. In this article, we investigate the Equity-Indexed annuities valuation when the discrete dividend payments follow a Markov-modulated jump diffusion model. Using the generalized Itô formula, we obtain the explicit solution for dividend payments of the model. From Dividend Discount theory, which implies that the stock price should be equal to the net present value of all its future dividend payments, the stock price process is then deduced. Within this framework, closed-form solution to the point-to-point EIA pricing problem is derived via the characteristic function of the occupation times.