Large Portfolio Asymptotics for Loss from Default
Mathematical Finance, Forthcoming
29 Pages Posted: 6 Sep 2011 Last revised: 4 Nov 2020
Date Written: October 17, 2013
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
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