Default risk, bankruptcy procedures and the market value of life insurance liabilities

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in DEPARTMENT OF STATISTICS UNIVERSITY OF BONNAbstract. 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 value 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 U.S. Bankruptcy Code with Chapter 7 and Chapter 11 bankruptcy procedures is used. Grosen and Jørgensen's (2002) 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.

Knightian uncertainty and insurance regulation decision

“…It should be pointed out that the barrier function B t (η, φ) can exhibit quite flexible patterns. It is observed that this time-varying barrier encompasses the exponential barrier given in Grosen and Jørgensen [2002], Chen and Suchanecki [2007] and Bernard and Chen [2008] by setting φ = g. Here, both η and φ can be used by the regulator to control the strictness of the auditing rule. A high η or a high φ would lead to a high barrier level.…”

“…Grosen andJørgensen [2000, 2002] extends the model by allowing possible default at any instant before maturity. Bernard, Le Courtois andQuittard-Pinon [2005, 2006] and Chen and Suchanecki [2007] further extend Grosen and Jørgensen by either incorporating stochastic interest rate or discussing more realistic bankruptcy procedures. In all the literature, the regulators act very passively in the sense of not taking any actions against the collapse of the insurance company when it runs into default.…”

A Closed-Form Extension to the Black-Cox Model

“…Let us mention here that other Black-Cox extensions based on analytical formulas for Parisian type options have been proposed in the recent past. Namely, Chen and Suchanecki [8], Moraux [14] and Yu [16] have considered the case where the default is triggered when the stock has spent a certain amount of time in a row or not under the barrier. Nonetheless, both extensions present the drawback that the default is actually predictable and the default intensity is either 0 or infinite.…”

Double-sided Parisian option pricing

“…The way Parisian options turn up in real option problems is treated in [11], for an application in the direction of convertible bonds see [18]. For applications in credit risk and life insurance see [19] and [6] respectively. The authors in [8] derived Laplace transforms for the single-sided version, which is extended in [11] to a Parisian type of contract that is triggered by staying a period of time above the barrier or hitting a level exceeding this barrier.…”