All Your Hedges in One Matrix
32 Pages Posted: 8 Dec 2011
Date Written: August 11, 2011
This paper presents a framework to model correlated default events that can be used to price and hedge standard and exotic credit baskets whose values depend on the realized losses of a default portfolio. The model consists of parametric continuous time Markov chain and aims to accurately capture the point-in-time dynamics of the credit worthiness of debt issuers, the single name dynamics, and the dynamics of the correlation among the names underlying the credit portfolio. Key features of the model are the implied credit rating and the local correlation as a function of the implied rating and time. We illustrate through an example how to price and hedge with this model standard CDO index tranches. This method is computationally fast and parsimonious because uses just one matrix. The framework is simple and at the same time very rich in information and this can easily accommodate for the evaluation of MBSs, CMOs and CDO of ABS tranches.
Keywords: implied credit rating, point-in-time credit dynamics, dynamic correlated defaults, local correlation, credit cycle, market state dependent recovery, credit risk premia, asymmetric variance gamma process, continuous time-inhomogeneous Markov chains, functional analysis
JEL Classification: C02, C51, C63, G11, G12
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