Pricing and risk management of variable annuities and equity-indexed annuities

A variety of equity-linked insurance contracts such as variable annuities (VA) and equity-indexed annuities (EIA) have gained their attractiveness in the past decade because of the bullish equity market and low interest rates. Due to the complexity of their inherent nature, pricing and risk management of these products are quantitatively challenging and therefore have become sources of concern to many insurance companies. From a financial engineer's perspective, the options in VA and those embedded in EIA can be modeled as puts and calls, respectively, and enable the use of numerical option pricing techniques. Additionally, values of VA and EIA move in opposite directions in response to changes in the underlying equity value. Therefore, for insurers who offer both businesses, there are natural offsets or diversification benefits in terms of economic capital (EC) usage. In this chapter, we consider two specific products: the guaranteed minimal account benefit (GMAB) and the point-to-point (PTP) EIA contract, which belong to the VA and EIA classes respectively. Taking into account mortality risk and suboptimal dynamic lapse behavior, we build a framework that quantifies the value of each product and the natural hedging benefits based on risk-neutral option pricing theory. With Monte Carlo simulation and finite difference methods being implemented, an optimum product mixture of those two contracts is achieved that deploys capital the most efficiently.