Guaranteed Annuity Options

Abstract

Under a guaranteed annuity option, an insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970's and 1980's when long-term interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990's, as long-term interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred.The emerging liabilities under these guarantees threatened the solvency of some companies and led to the closure of Equitable Life (UK) to new business. In this paper we explore the pricing and risk management of these guarantees.

Affine Stochastic Mortality

“…GAOs are treated in a number of papers in the literature, see Boyle and Hardy (2003) and Pelsser (2003) among others. A GAO gives the policyholder the right to convert an assured sum into an annuity at the maximum of the prevailing market annuity rate or a guaranteed annuity rate, say r G x .…”

“…One could then easily price several well studied options embedded in insurance contracts under stochastic mortality. Examples of such contracts are Guaranteed Annuity Options (GAOs) or Rate of Return Guarantees, see among others, Brennan and Schwartz (1976), Bacinello and Ortu (1993), Aase and Persson (1998), Boyle and Hardy (2003), Pelsser (2003) or Schrager and Pelsser (2004a).…”

Valuation of Guaranteed Annuity Options in Affine Term Structure Models

“…For the mortality risk, we assume that it is independent of the financial risk so that it is diversifiable. It is quite acceptable to use deterministic mortality for valuing options that are dependent on the death of the policyholder (Boyle and Hardy, 2003).…”

“…Boyle and Hardy (2003) provide an insightful review on the issues of pricing, reserving and hedging GAO's under interest rate risk, equity risk and mortality risk. Pelsser (2003) shows how to construct a replicating portfolio of interest rate swaptions that replicates the GAO.…”

Policyholder Exercise Behavior in Life Insurance: The State of Affairs

“…Second, when regulatory or economic circumstances change, relying on historical data may be deceptive. For instance, a rise in market interest rates in the 1970s resulted in the so-called disintermediation in the whole life market with drastically more surrenders and policy loans (Black and Skipper, 2000, p. 111); also, misjudgment of exercise of Guaranteed Annuity Options (GAOs) in the face of falling interest rates contributed to the demise of the UK-based life insurer Equitable Life in 2000 (Boyle and Hardy, 2003). Hence, it is necessary to have an understanding of what drives these empirical exercise rules-and, particularly, under which circumstances they may fail.…”