The Mathematics of Financial Models: Solving Real-World Problems with Quantitative Methods

CHAPTER 8 Valuing Variable Annuity Guarantees

In Chapter 5, I presented examples of exotic–option pricing that traded in the capital-markets arena. In this chapter, I will discuss an example of an exotic option that is couched as a retail investment product that is prevalent in the insurance industry. Known as variable annuities (VAs), these products are essentially mutual fund investments with performance guarantees that are linked to the time of death—hence making it possible to be manufactured only by life insurance companies.¹

VAs have been sold in the United States by life insurance companies since the late 1960s.^2,3 Although variable annuities were originally sold as mutual funds containing embedded death benefits (sometimes known as guaranteed minimum death benefits or GMDBs), in recent decades variable annuities have morphed to include living benefits (sometimes known as guaranteed minimum accumulation benefits or GMABs, guaranteed minimum income benefits or GMIBs, and guaranteed minimum withdrawal benefits or GMWBs). VAs have gained tremendous popularity with consumers so much so that in the U.S. market new annual sales volume easily exceeds USD$110 billion and the current total volume of the U.S. marketplace for such products far exceeds 1 trillion U.S. dollars—making it an important investment tool in any retiree's investment-product arsenal. The interested reader is referred to the classic 2009 reference on this topic by Kalberer and Ravindran for further details. ...