This paper is an expanded version of a previous paper titled “Diversification and Default Risk: An Equivalence Theorem for Martingale and Empirical Default Intensities.” We thank Jaksa Cvitanic, Darrell Duffie, Miguel Ferreira, Michael Gordy, Jean Jacod, Lionel Martellini, Fuvio Ortu, Ken Singleton, Fernando Zapatero, an anonymous referee, and seminar participants at Stanford, USC, UC-Irvine, PIMCO, the 2002 Credit Risk Summit, the 11th Derivative Securities Conference, the 2001 QMF Conference in Sydney, the 2001 Meeting of the European Finance Association, the 2000 Risk Management Conference at the NYU Salomon Center, and the 1999 Frank Batten Young Scholars Conference at the College of William and Mary for helpful comments. We also thank Jens Christensen for excellent research assistance. David Lando acknowledges the partial support of the Danish Social Science Foundation.
DEFAULT RISK AND DIVERSIFICATION: THEORY AND EMPIRICAL IMPLICATIONS
Article first published online: 10 JAN 2005
Volume 15, Issue 1, pages 1–26, January 2005
How to Cite
Jarrow, R. A., Lando, D. and Yu, F. (2005), DEFAULT RISK AND DIVERSIFICATION: THEORY AND EMPIRICAL IMPLICATIONS. Mathematical Finance, 15: 1–26. doi: 10.1111/j.0960-1627.2005.00208.x
Manuscript received December 2002; final revision received November 2003.
- Issue published online: 10 JAN 2005
- Article first published online: 10 JAN 2005
- default risk;
- default risk premium;
- empirical and martingale default intensities
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.