A Spot Recovery Rate Extension of the Gaussian Copula

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A Spot Recovery Rate Extension of the Gaussian Copula

by Norddine Bennani of Barclays Capital, and
Jerome Maetz of Barclays Capital

July 2009

Abstract: The market evolution since the end of 2007 has been characterized by an increase of the systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to trade with significant spread levels.

This has triggered a growing interest for stochastic recovery modelling. This paper presents an extension to the standard Gaussian copula framework that introduces a consistent modelling of stochastic recovery. We choose to model directly the spot recovery, which allows to preserve time consistency, and compare this approach to the standard ones, defined in terms of recovery to maturity. Taking a specific form of the spot recovery function, we show that the model is flexible and tractable, and easy to calibrate to both individual credit spread curves and index tranche markets. Through practical numerical examples, we analyze specific model properties, focusing on default risk.

JEL Classification: G12, G13, C02.

Keywords: stochastic recovery, CDO, correlation smile, base correlation, copula, factor model, default risk.

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