خطرات پیش فرض، مراحل ورشکستگی و ارزش بازار بدهی بیمه عمر

The topic of insolvency risk in connection with life insurance companies has recently attracted a great deal of attention. In this paper, the question is investigated of how the values of the equity and of the liability of a life insurance company are affected by the default risk and the choice of the relevant bankruptcy procedure. As an example, the US Bankruptcy Code with Chapter 7 and Chapter 11 bankruptcy procedures is used. Grosen and Jørgensen’s [Grosen, A., Jørgensen, P.L., 2002. Life insurance liabilities at market value: An analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. J. Risk Insur. 69 (1), 63–91] contingent claim model, implying only a Chapter 7 bankruptcy procedure, is extended to allow for more general bankruptcy procedures such as Chapter 11. Thus, more realistically, default and liquidation are modelled as distinguishable events. This is realized by using so-called standard and cumulative Parisian barrier option frameworks. It is shown that these options have appealing interpretations in terms of the bankruptcy mechanism. Furthermore, a number of representative numerical analyses and comparative statics are performed in order to investigate the effects of different parameter changes on the values of the insurance company’s equity and liability, and hence on the value of the life insurance contract. To complete the analysis, the shortfall probabilities of the insurance company implied by the proposed models are computed and compared.

The topic of insolvency risk in connection with life insurance companies has recently attracted a great deal of attention. Since the 1980s a long list of defaulted life insurance companies in Europe, Japan and the United States has been reported. A few examples from the United States are First Farwest Corp., Integrated Resource Life Insurance Co. and Pacific Standard Life Insurance Co. in 1989, Mutual Security Life Insurance Co. in 1990, First Executive Life Insurance Co. (this constituted the 12th largest bankruptcy in the United States in the period 1980–2005), First Stratford Life Insurance Co., Executive Life Insurance Company of New York, Fidelity Bankers Life Insurance Co., First Capital Life Insurance Co., Mutual Benefit Life Insurance Co. and Guarantee Security Life Insurance Co. in 1991, Fidelity Mutual Life Insurance Co. in 1992, Summit National Life Insurance Co., Monarch Life Insurance Co. and Confederation Life Insurance Co. in 1994, ARM Financial Group in 1999, Penn Corp. Financial Group in 2000, Conseco Inc. in 2002 (this constituted the 3rd largest bankruptcy in the United States in the period 1980–2005)1 and Metropolitan Mortgage & Securities in 2004.2Table 1 provides more detailed information on the bankruptcy procedure and the number of days spent in default for some exemplary bankruptcies of life insurance companies in the United States

In the present article, we extend the model of Grosen and Jørgensen (2002) and investigate the question of how to value an equity-linked life insurance contract when considering the default risk (and the liquidation risk) under different bankruptcy procedures. In order to take into account the realistic bankruptcy procedure Chapter 11, these risks are modelled in both standard and cumulative Parisian frameworks. In the numerical analysis part, we perform several sensitivity analyses to see how the fair combinations of the participation rate and the minimum interest rate guarantee depend on the volatility of the company’s assets, the maturity dates of the contract, the regulation parameter and the length of excursion. In addition, due to their importance, a number of tables are given which help to catch and to compare the effects of the two regulation parameters dd and ηη. Furthermore, we consider how likely it is that the liability holder will obtain the rebate payment whose size is uncertain at the point in time when the contract is signed. Based on the analysis in Section 4, the insurance company can offer different contracts to customers with different willingness to accept certain shortfall probabilities.