Academic journal article Journal of Risk and Insurance

Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

Academic journal article Journal of Risk and Insurance

Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

Article excerpt

ABSTRACT

This article takes a contingent claim approach to the market valuation of equity and liabilities in life insurance companies. A model is presented that explicitly takes into account the following: (i) the holders of life insurance contracts (LICs) have the first claim on the company's assets, whereas equity holders have limited liability; (ii) interest rate guarantees are common elements of LICs; and (iii) LICs according to the so-called contribution principle are entitled to receive a fair share of any investment surplus. Furthermore, a regulatory mechanism in the form of an intervention rule is built into the model. This mechanism is shown to significantly reduce the insolvency risk of the issued contracts, and it implies that the various claims on the company's assets become more exotic and obtain barrier option properties. Closed valuation formulas are nevertheless derived. Finally, some representative numerical examples illustrate how the model can be used to establish the set of initially fair contracts and to determine the market values of contracts after their inception.

INTRODUCTION

The subject of fair valuation of life insurance liabilities has attracted a lot of attention in the insurance and finance literature in recent years. This is caused by the product structure of the life insurance business as well as certain events in the financial markets.

The late 1980s through the 1990s was a period of quite some turmoil for the life insurance business, and Europe, Japan, and the United States can all present their own spectacularly long lists of defaulted life insurance companies. Many of these were relatively small, but some massive defaults of large economic significance also occurred including the United States' First Executive Corporation ($19 billion in assets), France's Garantie Mutuelle des Functionnaires (see Briys and de Varenne, 1994), and Nissan Mutual Life of Japan, which went bankrupt with uncovered liabilities of $2.56 billion (see Grosen and Jorgensen, 2000).

In retrospective discussions of the reasons for these unfortunate events, three issues appear repeatedly. The first is the mismanagement of the interest rate guarantees issued with most life insurance policies. The second is the mismanagement of credit risk stemming from either side of the balance sheet, and the third relates to the application of poor or inappropriate accounting principles, which in many cases have critically delayed or suppressed potentially useful warning signs in relation to company solvency. These issues are, of course, closely interrelated, as will be further clarified in the subsequent discussion.

The focus on the interest rate guarantee relates to the fact that most policies contain an explicit guarantee that the holder's account will be credited--on a year-to-year basis--with a rate of return (the policy interest rate) of at least some fixed guaranteed rate, say, 5 percent. At the time of issuance, the guaranteed interest rate has typically been (much) lower than prevailing market interest rates, a fact that has led companies to ignore their value (as well as their risk), and, to the best of the authors' knowledge, premiums for these issued guarantees (read: liabilities) have not been demanded anywhere before 1999. (1) However, as a result of a period when market interest rates have generally been declining and when guaranteed interest rates have been held fixed, the companies have experienced a dramatic narrowing in the safety margin between the earning power of their assets and the claims from issued liabilities. This particular development is a major source of the problems of some life insurance c ompanies, although it is also a bit ironic, because the fundamental function of insurance companies in general is to provide a guaranty of asset value to the customer, as pointed out by, e.g., Merton and Bodie (1992). Interest rate guarantees are thus a source of credit risk arising from the liability side of the balance sheet. …

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