Academic journal article Journal of Risk and Insurance

Valuation of Early Exercisable Interest Rate Guarantees

Academic journal article Journal of Risk and Insurance

Valuation of Early Exercisable Interest Rate Guarantees

Article excerpt


This article focuses on the valuation of financial contracts that entail an explicit interest rate guarantee. In particular, we concentrate on interest rate guarantees with the possibility of premature or early exercise. The contract in question is arranged between two agents. An investor makes a deposit with a fund manager, who invests in a definite reference portfolio and guarantees a certain minimum return on the investment. The guarantee applies until the maturity date of the contract, but the investor may decide to invoke the guarantee prematurely if doing so is advantageous.

An arrangement of this sort is an explicit or implicit characteristic of many products in the financial markets as well as in the insurance industry. Because of the early exercise feature of the guarantee element, the financial economist will quickly recognize the similarity between the above contract and American options, which can be exercised at any time until maturity - contrary to European options, which can be exercised at maturity only.

For the actuary, the early exercise feature brings to mind the surrender feature or sell-back option of some life insurance products. In particular, the contract has characteristics in common with unit-linked or equity-linked life insurance policies (ELLIPs) with interest rate guarantees included.

This article examines the intersection between the financial and the actuarial sciences and attempts to apply some recent option theoretical results in order to obtain a market-based valuation of contracts linked to some reference portfolio (the unit) and with an American type of interest rate guarantee added.

Previous literature in this area reflects the fact that the option to exercise early - the surrender feature - has not been a common element of unit-linked life insurance products. For example, Brennan and Schwartz (1976) obtain equilibrium prices for the most common ELLIPs by an application of European option pricing theory.(1) The analogy between European options and guaranteed ELLIPs is further developed in subsequent articles by Boyle and Schwartz (1977), Brennan and Schwartz (1979), Collins (1982), Nielsen and Sandmann (1994), Ekern and Persson (1995), and Aase and Persson (1997).

However, ELLIPs with an American type of interest rate guarantee do in fact exist. In Norway, for example, a variety of these types of policies are offered by major insurance companies, and, in Denmark, banks have recently been offering their clients participation in investment programs with contract characteristics that are very similar to the contracts that we study here.(2)

Furthermore, since the option to exercise early is an embedded characteristic in many traditional life insurance contracts, our model may prove helpful in the valuation of other contracts - or elements of contracts - which, to a reasonable degree of accuracy, can be approximated as a pure American type of ELLIP.

Our motivation for the present article was further nourished by the observation that, in the last twenty years, there has been a dramatic drop in the safety margin between the earning power of the insurance companies and the issued interest rate guarantees leading to potential solvency problems. In response to this development, many companies have lowered the level of their guaranteed interest rates. Other companies have responded to the potential solvency problems by changing the type of option implicit in the interest rate guarantee from American to European. As a result, it is now quite common that the insurance companies have policyholders with different types of interest rate guarantees in the same fund. Ignorance of the fair valuation of these guarantees will naturally lead to an inequitable treatment of different classes of policyholders. We provide some numerical results which illustrate that the redistribution of wealth among the various classes of policyholders stemming from incorrect pricing of the guarantees can be substantial. …

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