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date: 04 August 2020

Abstract and Keywords

This article gives an account of mathematical techniques for credit risk models where there is contagion between the obligors, i.e., default of one party either directly causes default of other parties or (more commonly) changes other parties' risk of default. Section 2 starts with a general discussion of joint distributions and copulas, mainly to point out that ‘contagion’ is in some sense already built into the copula concept. Section 3 gives a general formulation of the reduced-form model and a taxonomy of models distinguishing between factor, frailty, and contagion models. Section 4 gives some background information about Markov processes, Markov chains, and phase-type distributions as required for the subsequent sections. Section 5 discusses four simple but effective Markov chain-based models with applications in counterparty risk and credit risk for inhomogeneous and homogeneous portfolios. Sections 6 and 7 develop the ‘subsidiary themes’ mentioned above. Section 8 returns to the further development of the Enhanced Risk homogeneous portfolio model, introduced in Section 5.4, in the light of these themes.

Keywords: credit risk models, contagion, obligors, copula, Markov chain, Enhanced Risk

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