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Affine Point Processes and Portfolio Credit Risk

29 Pages Posted: 14 Jun 2006 Last revised: 15 Jun 2010

Eymen Errais

Stanford University

Kay Giesecke

Stanford University - Management Science & Engineering

Lisa R. Goldberg

University of California, Berkeley; Aperio Group

Date Written: June 7, 2010


This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are self- and cross-exciting, and facilitate the description of complex event dependence structures. Ordinary differential equations characterize the transform of an affine point process and the probability distribution of an integer-valued affine point process. The moments of an affine point process take a closed form. This guarantees a high degree of computational tractability in applications. We illustrate this in the context of portfolio credit risk, where the correlation of corporate defaults is the main issue. We consider the valuation of securities exposed to correlated default risk, and demonstrate the significance of our results through market calibration experiments. We show that a simple model variant can capture the default clustering implied by index and tranche market prices during September 2008, a month that witnessed significant volatility.

Keywords: Self-exciting point process, affine jump diffusion, Hawkes process, transform, portfolio credit derivative, correlated default, index and tranche swap

JEL Classification: C00, C13, C14, C51, C53, G12, G13, G33

Suggested Citation

Errais, Eymen and Giesecke, Kay and Goldberg, Lisa R., Affine Point Processes and Portfolio Credit Risk (June 7, 2010). Available at SSRN: or

Eymen Errais

Stanford University ( email )

Stanford, CA 94305
United States

Kay Giesecke

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States
(650) 723 9265 (Phone)
(650) 723 1614 (Fax)


Lisa R. Goldberg (Contact Author)

University of California, Berkeley ( email )

Department of Statistics
367 Evans Hall
Berkeley, CA 94720-3860
United States

Aperio Group ( email )

3 Harbor Drive
Suite 315
Sausalito, CA 94965
United States

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