ارزیابی منصفانه از تعهدات بیمه عمر: تاثیر تضمین نرخ بهره، گزینه های تسلیم، و سیاست های جایزه
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|24069||2000||21 صفحه PDF||سفارش دهید||10887 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Insurance: Mathematics and Economics, Volume 26, Issue 1, 1 February 2000, Pages 37–57
The paper analyzes one of the most common life insurance products — the so-called participating (or with profits) policy. This type of contract stands in contrast to unit-linked (UL) products in that interest is credited to the policy periodically according to some mechanism which smoothes past returns on the life insurance company’s (LIC) assets. As is the case for UL products, the participating policies are typically equipped with an interest rate guarantee and possibly also an option to surrender (sell-back) the policy to the LIC before maturity. The paper shows that the typical participating policy can be decomposed into a risk free bond element, a bonus option, and a surrender option. A dynamic model is constructed in which these elements can be valued separately using contingent claims analysis. The impact of various bonus policies and various levels of the guaranteed interest rate is analyzed numerically. We find that values of participating policies are highly sensitive to the bonus policy, that surrender options can be quite valuable, and that LIC solvency can be quickly jeopardized if earning opportunities deteriorate in a situation where bonus reserves are low and promised returns are high.
Embedded options pervade the wide range of products offered by pension funds and life insurance companies. Interest rate guarantees, bonus distribution schemes, and surrender possibilities are common examples of implicit option elements in standard type policies issued in the United States, Europe, as well as in Japan. Such issued guarantees and written options are liabilities to the issuer. They represent a value and constitute a potential hazard to company solvency and these contract elements should therefore ideally be properly valued and reported separately on the liability side of the balance sheet. But historically this has not been done, to which there are a number of possible explanations. Firstly, it is likely that some companies have failed to realize that their policies in fact comprised multiple components, some of which were shorted options. Secondly, it seems fair to speculate that other companies have simply not cared. The options embedded in their policies may have appeared so far out of the money, in particular at the time of issuance, that company actuaries have considered the costs associated with proper assessment of their otherwise negligible value to far outweigh any benefits. Thirdly, the lack of analytical tools for the evaluation of these particular obligations may have played a part. Whatever the reason, we now know that the negligence turned out to be catastrophic for some companies, and as a result shareholders and policyowners have suffered. In the United States, a large number of companies have been unable to meet their obligations and have simply defaulted (see e.g. Briys and de Varenne, 1997 and the references cited therein for details), whereas in e.g. the United Kingdom and Denmark, companies have started cutting their bonuses in order to ensure survival. The main trigger for these unfortunate events is found on the other side of the balance sheet where life insurance companies have experienced significantly lower rates of return on their assets than in the 1970s and 1980s. The lower asset returns in combination with the reluctance of insurance and pension companies to adjust their interest rate guarantees on new policies according to prevailing market conditions have resulted in a dramatic narrowing of the safety margin between the companies’ earning power and the level of the promised returns. Stated differently, the issued interest rate guarantees have moved from being far out of the money to being very much in the money, and many companies have experienced solvency problems as a result. The reality of this threat has most recently been illustrated in Japan where Nissan Mutual life insurance group collapsed as the company failed to meet interest rate guarantees of 4.7% p.a. 2 Nissan Mutual’s uncovered liabilities were estimated to amount to $2.56 billion, so in this case policyholders’ options indeed expired in the money without the company being able to fulfil its obligations. Partly as a result of Nissan Mutual Life’s collapse, Japanese life insurance companies have been ordered to reduce the interest rate guarantee from 4.5% to 2.5% p.a. In Europe, the EU authorities have also responded to the threat of insolvency from return guarantees. Specifically, Article 18 of the Third EU Life Insurance Directive, which was effective as of 10 November, 1992, requires that interest rate guarantees do not exceed 60% of the rate of return on government debt (of unspecified maturity). In relation to this, Table 1 shows the prevalent maximum level of interest rate guarantees as of October 1998 for Japan and the EU member countries. In several of these countries, the maximum guaranteed interest rate has decreased during recent years and further cuts are likely to be seen.3As a consequence of the problems outlined above, insurance companies have experienced an increased focus on their risk management policy from regulatory authorities, academics, and the financial press. In particular the shortcomings of traditional deterministic actuarial pricing principles when it comes to the valuation of option elements are surfacing. Recent years have also revealed an increasing interest in applying financial pricing techniques to the fair valuation of insurance liabilities, see for example Babbel and Merrill, 1999, Boyle and Hardy, 1997 and Vanderhoof and Altman, 1998.4 In the literature dealing with the valuation of and to some extent also the reserving for insurance liabilities, several types of contracts and associated guarantees and option elements are recognized. Some of the contracts considered contain option elements of European type, meaning that the option(s) can be exercised only at maturity. This contrasts American type contracts where the embedded option(s) can be exercised at any time during the life of the contract. Another important distinction must be made between unit-linked contracts 5 and contracts where interest is credited according to some smoothing surplus distribution mechanism. The latter type is generally known as participating contracts and the interest rate crediting mechanism applied is often referred to as a portfolio average method or an average interest principle. Finally, in relation to guarantees it is important to distinguish between maturity guarantees and interest rate guarantees (rate of return guarantees). A maturity guarantee is a promise to repay at least some absolute amount at maturity (75% of the initial deposit, say) whereas an interest rate guarantee promises to credit the account balance with some minimum return every period. 6 While participating policies are by far the most important in terms of market size, the larger part of the previous literature in this area has been analyzing unit-linked contracts with interest rate or maturity guarantees of the European type (Baccinello and Ortu, 1993a, Baccinello and Ortu, 1993b, Boyle and Hardy, 1997, Boyle and Schwartz, 1977, Brennan and Schwartz, 1976, Brennan and Schwartz, 1979 and Nielsen and Sandmann, 1995). Some notable exceptions to this are the works by Brennan, 1993, Briys and de Varenne, 1997, Grosen and Jørgensen, 1997 and Miltersen and Persson, 1998. Inspired by classic UK with profits policies, Brennan (1993) discusses the efficiency costs of the reversionary bonus mechanism applied to these contracts. In their analysis of the valuation and duration of life insurance liabilities, Briys and de Varenne (1997) explicitly introduce a participation level in addition to the guaranteed interest rate attached to policies. However, the model is essentially a single period model where distinctions between interest rate and maturity guarantees and between guarantees of European and American type become less interesting. Miltersen and Persson (1998) present another interesting model in which contracts with an interest rate guarantee and a claim on excess returns can be valued. To model a kind of participation, the authors introduce a bonus account to which a part of the return on assets is distributed in ‘good’ years and from which funds can be withdrawn and used to fulfil the interest rate guarantee in poor years. The drawbacks of this model are that no averaging or smoothing is built into the distribution mechanism, and that the bonus account, if positive at maturity, is paid out in full to policyholders. This is a somewhat unrealistic assumption. Also the American type surrender option is not considered in this model. In Grosen and Jørgensen (1997), arbitrage-free prices of unit-linked contracts with an early exercisable (American) interest rate guarantee are obtained by the application of American option pricing theory. They also point out that the value of the option to exercise prematurely is precisely the value of the surrender option implicit in many life insurance contracts. The numerical work in Grosen and Jørgensen (1997) demonstrates that this particular option element may have significant value and hence that it must not be overlooked when the risk characteristics of liabilities are analyzed and reserving decisions are made. However, the contracts considered in their paper are unit-linked and bonus mechanisms are not considered. The present paper attempts to fill a gap in the existing literature by extending the analysis in Grosen and Jørgensen (1997) from unit-linked contracts to traditional participating policies, i.e. to contracts in which some surplus distribution mechanism is employed each period to credit interest at or above the guaranteed rate. The objective is thus to specify a model which encompasses the common characteristics of life insurance contracts discussed above and which can be used for valuation and risk analysis in relation to these particular liabilities. Our work towards this goal will meet a chain of distinct challenges: First, asset returns must be credibly modeled. In this respect we take a completely non-controversial approach and adopt the widely used framework of Black and Scholes (1973). Second, and more importantly, a realistic model for bonus distribution must be specified in a way that integrates the interest rate guarantee. This is where our main contributions lie. The third challenge is primarily of technical nature and concerns the arbitrage-free valuation of the highly path-dependent contract pay-offs resulting from applying the particular bonus distribution mechanism suggested to customer accounts. We will carefully take interest rate guarantees as well as possible surrender options into account and during the course of the analysis we also briefly touch upon the associated problem of reserving for the liabilities. Finally, we provide a variety of illustrative examples. The numerical section of the paper also contains some insights into the effective implementation of numerical algorithms for solving the model. The paper is organized as follows. Section 2 describes the products which will be analyzed and presents the basic modeling framework. In particular, the bonus policy and the dynamics of assets and liabilities are discussed. In Section 3 we present the methodology applied for contract valuation, we demonstrate how contract values can be conveniently decomposed into their basic elements, and computational aspects are addressed. Numerical results are presented in Section 4, and Section 5 concludes the paper.
نتیجه گیری انگلیسی
As the general level of interest rates has dropped in the 1990s, life insurance companies have experienced a dramatic narrowing in the safety margin between their earning power on the asset side and the level of promised returns on the liability side. As a consequence, the interest rate guarantees issued with traditional participating life insurance policies have become particularly valuable to policyholders and threatened the solvency of the issuing companies. The situation has in many cases been worsened by established bonus practices and by the fact that some contracts have been issued with an option to surrender the policy before maturity. Life insurance companies have traditionally not given much attention to the proper valuation of the various option elements with which their policies have been issued, and this has undoubtedly contributed to the problems now experienced in the life insurance business. In the present paper we have presented a dynamic model for use in valuing the common family of life insurance products known as participating contracts. The model is based on the well-developed theory of contingent claims valuation. We have shown that the typical contract can be decomposed into three basic elements: a risk free bond, an option to receive bonus, and a surrender option. The properties of the model were explored numerically. The analysis showed that contract values are highly dependent on the assumed bonus policy and on the spread between the market interest rate and the guaranteed rate of interest built into the contract. In another application of the model, we estimated by simulation the relation between bonus policies and the probability of default at the individual contract level. This analysis showed default probabilities of substantial size for realistic parameter choices indicating that the management of the life insurance company should take solvency problems very seriously. In this respect, initiatives on both the asset and the liability sides could be considered. An obvious first choice could be to reduce asset volatility by changing the asset composition towards less risky assets. But another potential problem enters here. The return offered by less risky assets (bonds) might be so low that such a move would only make it certain that interest guarantees could not be honored in the future. A classical asset substitution problem where the company management is forced into taking risks might thus exist. Alternatively, to reduce the probability of default, the company could consider more conservative bonus policies to the extent that this is permitted by law and the contractual terms. In fact, the possibility for the management to change the bonus policy parameters in a sense constitutes a counter option which we have not explicitly taken into account in this paper. This is an interesting subject for future research as would be the analysis of how the asset mix could possibly be optimally described as a function of the liability situation of the life insurance company. Some other natural paths for further research emerge. In the present article, a model was constructed in order to describe actual insurance company behavior with particular respect to applied accounting principles and bonus policies. Future research should try to establish the ideal way in the sense that systematic market value accounting should constitute the basis of the balance sheet as well as the bonus policy. Furthermore, realism could obviously be added to the model by considering periodic premiums and taking into account mortality, lapses and various expense charges. Lastly, an interesting issue would be to incorporate the possibility of default of the life insurance company and to analyze how this would affect contract values and possibly also the optimal surrender strategy.