In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs. Generally,The risk-neutral default intensity it Q is not equal to the empirical or actual default intensity ),. This paper proves that multiple default intensities are invariant under equivalent martingale transformation,given a well-diversified portfolio corresponding to the defaultable bond. Thus one can directly apply default intensities and fractional losses empirically estimated to the evaluation of defaultable bonds or contingent claims. § 1 IntroductionA new approach to the pricing of credit risk called the "reduce-form" approach has been developed in the recent papers [1'2]. This approach is applicable to the pricing of the credit risk in various defaultable claims such as corporate bonds swap contracts,credit default swaps and credit spread options. Under some technical assumptions, Duffle and Singleton E2] showed that the defaultable zero-coupon bond with 1 dollar's payoff at maturity may be priced as if it were default-free by replacing the usual short-term interest rate process rt with default-adjusted short rate process R,=r,+2~l,. That is v(t,T) = E~{exp[--f:R,ds] }, (]. 1)where E~ denotes risk-neutral,conditional expectation at date t,),,Q is exogenous default intensity under risk-neutral probability and It denotes the expected fractional loss in market value if default occurs at time t. A key feature of the evaluation equation is that,provided we take the mean-loss rate ),Ql to be given exogeneously,the standard term-structure models for default-free debt are directly applicable to defaultable debt by parameterizing R instead of r. The result is powerful,though the model neglects the possibility that a firm's default may result in other firms defaulting.In this paper,a generalized defaultable bond pricing formula is presented by assuming Received : 2001-01-05. MR Subject Classification : 91B28,91B30,91B70.
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