Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model

Abstract

Fractional Brownian motion with Hurst exponent $H\in (1/2,1)$ is a good candidate for modeling financial time series with long-range dependence and self-similarity. The main purpose of this paper is to address the valuation of equity indexed annuity (EIA) designs under the market driven by fractional Brownian motion. As a result, this paper presents an explicit pricing expression for point-to-point EIA design and bounds for the pricing of high-water-marked EIA design. Some numerical examples are given to illustrate the impact of the parameters involved in the pricing problems.