Large Portfolio Asymptotics for Loss from Default

Mathematical Finance, Forthcoming

29 Pages Posted: 6 Sep 2011 Last revised: 4 Nov 2020

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Management Science & Engineering

Konstantinos Spiliopoulos

Brown University - Division of Applied Mathematics

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: October 17, 2013

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 stochastic PDE, and certain 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.

Keywords: law of large numbers, loss distribution, interacting point processes, portfolio credit risk

Suggested Citation

Giesecke, Kay and Spiliopoulos, Konstantinos and Sowers, Richard and Sirignano, Justin, Large Portfolio Asymptotics for Loss from Default (October 17, 2013). Mathematical Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1923125 or http://dx.doi.org/10.2139/ssrn.1923125

Kay Giesecke (Contact Author)

Stanford University - Management Science & Engineering ( email )

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

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

Konstantinos Spiliopoulos

Brown University - Division of Applied Mathematics ( email )

Providence, RI 02912
United States

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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