Counterparty Risk and the Pricing of Defaultable Securities

Abstract

Motivated by recent financial crises in East Asia and the United States where the downfall of a small number of firms had an economy-wide impact, this paper generalizes existing reduced-form models to include default intensities dependent on the default of a counterparty. In this model, firms have correlated defaults due not only to an exposure to common risk factors, but also to firm-specific risks that are termed "counterparty risks." Numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps.

A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap

“…Corollary 1 Under the assumption of Proposition 1, if b 1 = c 1 = 0, then the joint distribution of default times (τ B , τ C ) with the default intensity defined by (1) and (2) …”

“…Take (17), (18) and (20) into (14), we can get Proposition 2 Assume that the default buyer does not default during the entire contract, and that the default intensities of B (the protection seller) and C (reference asset) are given by (1 ) and (2 ), then the swap premium is given by…”

“…As remarked by Jarrow and Yu [1] , an investigation of counterparty risk is incomplete without studying its impact on the pricing of credit derivatives. The reference issuers and the derivative issuers not only have individual default risk, but also correlate in some way.…”

“…The last approach to model default correlation, contagion model, relies on the works by Davis and Lo [8] , and Jarrow and Yu [1] . It is based on the idea of default contagion, in which, when a firm defaults, the default intensities of related firms jump upwards.…”

“…Leung and Kwok [9] gave the analytic solution for the CDS premium for the model in Ref. [1] by employing the change of measure which was introduced in Ref. [10].…”