Premium
LARGE PORTFOLIO ASYMPTOTICS FOR LOSS FROM DEFAULT
Author(s) -
Giesecke Kay,
Spiliopoulos Konstantinos,
Sowers Richard B.,
Sirignano Justin A.
Publication year - 2015
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12011
Subject(s) - stochastic differential equation , portfolio , monte carlo method , mathematics , limiting , measure (data warehouse) , nonlinear system , partial differential equation , mathematical optimization , statistical physics , computer science , mathematical analysis , physics , economics , statistics , finance , mechanical engineering , quantum mechanics , database , engineering
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.