Pricing equity-indexed annuities with path-dependent options

Equity-linked products such as equity-indexed annuities (EIAs) provide their customers with the greater of either the return linked to the underlying index or the minimum guaranteed return. The current volatile equity market increases the costs of options embedded in these products, and decreases the participation rates. This paper proposes four types of EIAs embedded with path-dependent options in order to increase participation rates. It also derives the joint distribution function of terminal time value and running maximum of Brownian motion. With the method of Esscher transforms, explicit pricing formulas for these proposed products and a floating-strike lookback option are derived.