LARGE PORTFOLIO ASYMPTOTICS FOR LOSS FROM DEFAULT
By Kay Giesecke, Konstantinos Spiliopoulos, Richard B. Sowers, Justin A. Sirignano. 2011
75 citations recorded by the source corpus.
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.
Subfields: Finance
View Paper: https://www.semanticscholar.org/paper/8792e971598f3d0f5469f382dc528a697dc224f7
How researchers see this paper
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In Finance
- Justin A. Sirignano
- Konstantinos Spiliopoulos
- Luciano Campi
- Mykhaylo Shkolnikov
- Sergey Nadtochiy
- Markus Fischer
- Daniel Lacker
- Rama Cont
Citations in the corpus
- $N$-player games and mean-field games with absorption (2016, background): “[20], a point process model of correlated defaults timing in a portfolio of firms has been introduced.”
- Mean Field Analysis of Neural Networks: A Law of Large Numbers (2018, methodology): “Weak convergence analysis has been widely used in other fields (for example, see [18], [19], [12], [13], [14], [6], and [23] for a nonexhaustive list).”
- Particle systems with singular interaction through hitting times: Application in systemic risk modeling (2017, methodology): “ connection to a problem from neuroscience, and we use and extend some of the ideas developed therein to establish our results (for alternative models, with smooth interaction, we refer to [IT15] and [GSSS15]). In particular, the convergence of the N-particle system as N → ∞ (Theorem 2.3) is based o”
- Mean field analysis of neural networks: A central limit theorem (2018, methodology): “Weak convergence analysis has been widely used in other fields (for example, see [14], [15], [5], [6], [7], [4], and [17] for a non-exhaustive list).”