Large Portfolio Asymptotics for Loss from Default

by Kay Giesecke of Stanford University,
Konstantinos Spiliopoulos of Brown University,
Richard B. Sowers of University of Illinois at Urbana-Champaign, and
Justin A. Sirignano of Stanford University

September 7, 2011

Abstract: We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinite system of SDEs. The solution to this system leads to the distribution of the limiting portfolio loss, which we propose as an approximation to the loss distribution for a large portfolio. Numerical tests illustrate the accuracy of the approximation, and highlight its computational advantages over a direct Monte Carlo simulation of the original stochastic system.

AMS Classification: 91G40, 60F05, 60F10.

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