Pricing Credit from the Top Down with Affine Point Processes

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Pricing Credit from the Top Down with Affine Point Processes

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

September 5, 2007

Abstract: A portfolio credit derivative is a contingent claim on the aggregate loss of a portfolio of credit sensitive securities such as bonds and credit swaps. We propose an affine point process as a dynamic model of portfolio loss. The recovery at each default is random and events are governed by an intensity that is driven by affine jump diffusion risk factors. The portfolio loss itself is a risk factor so past defaults and their recoveries influence future loss dynamics. This specification incorporates feedback from events and a dependence structure among default and recovery rates. We show that it leads to analytically tractable transform based pricing, hedging and calibration of credit derivatives, which we illustrate for index and tranche swaps.

Keywords: Self-affecting point process, affine point process, Hawkes process, portfolio credit derivative, index swap, tranche, transform, random thinning, pricing, calibration, hedging.

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