Heterogeneous credit portfolios and the dynamics of the aggregate losses

Pra, Paolo Dai; Tolotti, Marco

doi:10.1016/j.spa.2009.03.006

Cited by 35 publications

(20 citation statements)

References 17 publications

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“…The use of interacting particle systems to study the behavior of default clustering in large portfolios is a growing area. In a mean-field model, Dai Pra, Runggaldier, Sartori and Tolotti [3] and Dai Pra and Tolotti [4] take the intensity of a constituent firm as a deterministic function of the percentage portfolio loss due to defaults. In a model with local interaction, Giesecke and Weber [13] take the intensity of a constituent firm as a deterministic function of the state of the firms in a specified neighborhood of that firm.…”

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confidence: 99%

Default clustering in large portfolios: Typical events

Giesecke¹,

Spiliopoulos²,

Sowers³

2013

Ann. Appl. Probab.

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We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all firms, and past defaults. We prove a law of large numbers for the default rate in the pool, which describes the "typical" behavior of defaults.Comment: Published in at http://dx.doi.org/10.1214/12-AAP845 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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confidence: 99%

Default clustering in large portfolios: Typical events

Giesecke¹,

Spiliopoulos²,

Sowers³

2013

Ann. Appl. Probab.

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“…Firstly, there is the network models for clustering and contagion that follow the earlier work of [1,15], see also [22] for a review. Secondly, there is the dynamic mean field type of models literature, see for example [5,6,13,17,21,7,23,18]. Thirdly, there is the reduced form credit and portfolio risk literature that is using intensity models of correlated default, [9,19,20,30,32,31].…”

Section: Introductionmentioning

confidence: 99%

Network Effects in Default Clustering for Large Systems

Spiliopoulos

Jia

2019

Applied Mathematical Finance

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We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution of the different components in the pool and from this we extract important information for quantities such as the loss rate in the overall pool as well as the mean impact on a given component from system wide defaults. A singular value decomposition of the adjacency matrix of the graph allows to coarse-grain the system by focusing on the highest eigenvalues which also correspond to the components with the highest contagion impact on the pool. Numerical simulations demonstrate the theoretical findings.arXiv:1812.07645v2 [q-fin.RM]

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“…In [15,16] rare event asymptotics for the loss distribution in the Gaussian copula model of portfolio credit risk and related importance sampling questions are studied. In a large deviations analysis of a mean field model in [3] the authors take the default intensity of a component in the pool to be a deterministic function of the percentage pool loss due to defaults, see also [4]. In [23], the authors establish a large time large deviations principle for an interacting system of affine point processes.…”

Section: Introductionmentioning

confidence: 99%

Default Clustering in Large Pools: Large Deviations

Spiliopoulos

Sowers²

2015

SIAM J. Finan. Math.

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We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system interact through the empirical default rate and via systematic effects that are common to all components. We establish the large deviations principle for the empirical default rate for such an interacting particle system. The rate function is derived in an explicit form that is amenable to numerical computations and derivation of the most likely path to failure for the system itself. Numerical studies illustrate the theoretical findings. An understanding of the role of the preferred paths to large default rates and the most likely ways in which contagion and systematic risk combine to lead to large default rates would give useful insights into how to optimally safeguard against such events.

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Heterogeneous credit portfolios and the dynamics of the aggregate losses

Cited by 35 publications

References 17 publications

Default clustering in large portfolios: Typical events

Default clustering in large portfolios: Typical events

Network Effects in Default Clustering for Large Systems

Default Clustering in Large Pools: Large Deviations

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