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Default Risk and Diversification: Theory and Empirical Implications

by Robert A. Jarrow of Cornell University,
David Lando of the University of Copenhagen, and
Fan Yu of the University of California, Irvine

January 2005

Abstract: Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity's diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of "diversifiable default risk." The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgage-backed securities.

Keywords: default risk, diversification, default risk premium, empirical and martingale default intensities.

Published in: Mathematical Finance, Vol. 15, No. 1, (January 2005), pp. 1-26.

Previously titled: Default Risk and Diversification: Theory and Applications

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