LARGE PORTFOLIO ASYMPTOTICS FOR LOSS FROM DEFAULT

Kay Giesecke · Konstantinos Spiliopoulos · Richard B. Sowers · Justin A. Sirignano

70 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

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.

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References

2006Multi-period corporate default prediction with stochastic covariates 2003A risk-factor model foundation for ratings-based bank capital rules 2007Common Failings: How Corporate Defaults Are Correlated 2005Credit contagion and aggregate losses 2001An analytic approach to credit risk of large corporate bond and loan portfolios 2005A note on the large homogeneous portfolio approximation with the Student-t copula 2009Large portfolio losses: A dynamic contagion model 2007LARGE DEVIATIONS IN MULTIFACTOR PORTFOLIO CREDIT RISK

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