
 Pricing kthtodefault Swaps Under Default Contagion: The matrixanalytic approach by Alexander Herbertsson of Göteborg University, and November 27, 2006 Abstract: We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is translated into a Markov jump process which represents the default status in the credit portfolio. This makes it possible to use matrixanalytic methods to derive computationally tractable closedform expressions for singlename credit default swap spreads and k^{ th }todefault swap spreads. We "semicalibrate" the model for portfolios (of up to 15 obligors) against market CDS spreads and compute the corresponding k^{ th }todefault spreads. In a numerical study based on a synthetic portfolio of 15 telecom bonds we study a number of questions: how spreads depend on the amount of default interaction; how the values of the underlying market CDSprices used for calibration influence k^{ th }todefault spreads; how a portfolio with inhomogeneous recovery rates compares with a portfolio which satisfies the standard assumption of identical recovery rates; and, finally, how well k^{ th }todefault spreads in a nonsymmetric portfolio can be approximated by spreads in a symmetric portfolio. JEL Classification: G33, G13, C2, C63, G32. AMS Classification: 60J75, 60J22, 65C20, 91B28. Keywords: Portfolio credit risk, intensitybased models, default dependence modelling, default contagion, CDS, kthtodefault swaps, Markov jump processes, Matrixanalytic methods. Books Referenced in this paper: (what is this?) 