Introductory Stochastic Analysis for Finance and Insurance

CHAPTER 7

APPLICATIONS IN INSURANCE

In this chapter, we illustrate how stochastic calculus may be applied for the valuation of insurance and annuity products and and in particular of those whose benefits are linked to the performance of the bond and equity markets. In Section 7.1, we consider Deferred Variable Annuities (VAs) that are essentially selected mutual funds wrapped with guaranteed death and living benefits. Variable Annuities are sold by North American insurance companies as tax-deferred retirement saving products. The yearly sales of variable annuities has recently reached $126 billion and the total assets are more than $994 billion, according to the 2004 Annuity Fact Book published by the National Association for Variable Annuities (NAVA). A similar savings product called Equity-Indexed Annuity (EIA) is also considered in this section. EIA’s are fixed annuities wrapped with guaranteed death and living benefits but they differ from Variable Annuities in terms of pricing method and asset management. Equity-Indexed Annuities were introduced in 1995 and have been gaining popularity in recent years. Sales were over $12 billion in 2003. For more details, see Lin and Tan (2003). Section 7.2 considers the valuation of guaranteed annuity options (GAOs). A guaranteed annuity option allows a pension policyholder to convert his or her account value into a life annuity at a fixed annuitization rate at retirement. Guaranteed annuity options have received considerable attentions ...