Large Portfolio Asymptotics for Loss from Default

38 Pages Posted: 17 Jan 2015

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Management Science & Engineering

Richard Sowers

University of Illinois at Urbana-Champaign - Department of Mathematics

Justin Sirignano

Imperial College London - Department of Mathematics; University of Illinois at Urbana-Champaign

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Date Written: January 2015

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 heterogeneous portfolios. The density of the limiting measure is shown to solve a nonlinear stochastic partial differential equation, and certain moments of the limiting measure are shown to satisfy an infinite system of stochastic differential equations. 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.

Keywords: law of large numbers, interacting point process, credit risk

Suggested Citation

Giesecke, Kay and Sowers, Richard and Sirignano, Justin, Large Portfolio Asymptotics for Loss from Default (January 2015). Mathematical Finance, Vol. 25, Issue 1, pp. 77-114, 2015, Available at SSRN: https://ssrn.com/abstract=2551091 or http://dx.doi.org/10.1111/mafi.12011

Kay Giesecke (Contact Author)

Stanford University - Management Science & Engineering ( email )

475 Via Ortega
Stanford, CA 94305
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(650) 723 9265 (Phone)
(650) 723 1614 (Fax)

HOME PAGE: http://https://giesecke.people.stanford.edu

Richard Sowers

University of Illinois at Urbana-Champaign - Department of Mathematics ( email )

1409 W. Green St.
Urbana, IL 61801
United States

HOME PAGE: http://www.math.uiuc.edu/~r-sowers/

Justin Sirignano

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

HOME PAGE: http://jasirign.github.io

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

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