Affine Point Processes and Portfolio Credit Risk

by Eymen Errais of the Creditex,
Kay Giesecke of the Stanford University, and
Lisa R. Goldberg of the MSCI Barra

September 2010

Abstract: 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. ODEs 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.

AMS Classification: 60-08, 60J99, 60G55, 90-08, 90B25.

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

Published in: SIAM Journal on Financial Mathematics, Vol. 1, (November 2010), pp. 642-665.

Previously titled: Pricing Credit from the Top Down with Affine Point Processes

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