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In Rememberance: World Trade Center (WTC)

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Dynamic Models of Portfolio Credit Risk: A simplified approach

by John Hull of the University of Toronto, and
Alan White of the University of Toronto

April 2008

Abstract: We propose a simple dynamic model that is an attractive alternative to the (static) Gaussian copula model. The model assumes that the hazard rate of a company has a deterministic drift with periodic impulses. The impulse size plays a similar role to default correlation in the Gaussian copula model. The model is analytically tractable and can be represented as a binomial tree. It can be calibrated so that it exactly matches the term structure of CDS spreads and provides a good fit to CDO quotes of all maturities. Empirical research shows that as the default environment worsens default correlation increases. Consistent with this research we find that in order to fit market data it is necessary to assume that as the default environment worsens impulse size increases. We present both a homogeneous and heterogeneous version of the model and provide results on the use of the calibrated model to value forward CDOs, CDO options, and leveraged super senior transactions.

Keywords: CDO, dynamic model, forward, option, LSS.

Published in: Journal of Derivatives, Vol. 15, No. 4, (Summer 2008), pp. 9-28.

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