Affine Point Processes and Portfolio Credit Risk

TLDR

Affine point processes are self‑ and cross‑exciting, enabling modeling of complex event dependence structures. The study analyzes multivariate point process models driven by affine jump diffusion and applies them to portfolio credit risk, focusing on default correlation. The authors use ODEs to characterize the transform and distribution of affine point processes, and evaluate securities with correlated default risk through market‑calibration experiments. Closed‑form moments yield high computational tractability, and the model captures default clustering observed in September 2008 index and tranche prices.

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.