A Note on the Correlation Smile

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A Note on the Correlation Smile

by Svenja Hager of Eberhard-Karls University, and
Rainer Schöbel of Eberhard-Karls University

December 2006

Abstract: The correct modeling of default dependence is essential for the valuation of multiname credit derivatives. However for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations, default intensities and recovery rates for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opinion there wouldn't be the implied correlation smile that is observed in the market. The purpose of this paper is to explain the structure of the smile by discussing the influence of different correlation matrices on CDO spreads.

JEL Classification: G13.

Keywords: default risk, CDOs, implied correlation smile, correlation matrix, heterogeneity.

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