The Valuation Of Unilateral Default Contagion In Credit Risk

Motivated by recent financial crises in East Asia and the U.S. where the downfall of a small number of firms had an economy-wide impact, based on the current literature on default risk modeling this paper generalizes existing reduced-form models to include default intensities dependent on the default of a counterparty.Firstly, this paper introduces the unilateral default contagion model, in this model, there are two kinds of firms: primary and secondary firms. The default intensities of primary firms depend only on common factors, where the intensities of secondary firms depend not only on common factors, but also on the intensities of primary firms. For sake of convenient, this paper only focuses on the two firms' case, that is, firm A is the primary, firm B is the secondary.Secondly, based on the unilateral default contagion model, this paper deprives the joint distribution of the default times from the financial mathematics theories, such as the probability, measure theory, stochastic analysis, etc.At last, focused on the basket credit derivatives, this paper apply the joint distribution above to the classic risk-neutral valuation, especially, generalizes the pricing formula of the first-to-default contract and the last-to-default contract in the unilateral default contagion model.