ارزش بازار قراردادهای بیمه زندگی تحت نرخ بهره برداری تصادف و ریسک پیش فرض

The purpose of this article is to value some life insurance contracts in a stochastic interest rate environment taking into account the default risk of the underlying insurance company. The participating life insurance contracts considered here can be expressed as portfolios of barrier options as shown by Grosen and Jørgensen [J. Risk Insurance 64 (3) (1997) 481–503]. In order to price these options, the Longstaff and Schwartz [J. Finance 50 (3) (1995) 789–820] methodology is used with the Collin-Dufresne and Goldstein [J. Finance 56 (5) (2001) 1929–1957] correction.

Life insurance companies offer complex contracts written with the following many covenants: interest rate guarantees, bonus and surrender options, equity-linked policies, choice of a reference portfolio, participating policies. Each particular covenant has a value and is part of the company liabilities. These embedded options should not be ignored and must be priced. Many life-insurance companies, having neglected them for a long time, increased the difficulties they faced in the 1990s.

In this article we have proposed a new method to value typical participating life insurance contracts, with minimum guaranteed rate, in the presence of default risk, and in a stochastic interest rate environment. We have determined the fair participating level, which is a delicate and important point for a life insurance company. We have also analyzed the sensitivity of the main parameters to volatility. The suggested method relies on Fortet’s equation (1943) giving the first passage time of the assets process to the default barrier, and consequently paving the way for computing diverse exotic options embedded in the contract involving this random time