Marshall-Olkin Multivariate Exponential Distributions, Multidimensional Subordinators, Efficient Simulation, and Applications to Credit Risk

Sun, Yunpeng; Mendoza-Arriaga, Rafael; Linetsky, Vadim

doi:10.2139/ssrn.1702087

Cited by 9 publications

(12 citation statements)

References 42 publications

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“…t , which is basically just a complicated way of writing the original Marshall-Olkin shock model (2). This construction is not unique and provides an alternative proof of [Sun et al (2012) …”

Section: Proofmentioning

confidence: 98%

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Consistent Iterated Simulation of Multi-Variate Default Times: A Markovian Indicators Characterization

2013

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We investigate under which conditions a single simulation of joint default times at a final time horizon can be decomposed into a set of simulations of joint defaults on subsequent adjacent sub-periods leading to that final horizon. Besides the theoretical interest, this is also a practical problem as part of the industry has been working under the misleading assumption that the two approaches are equivalent for practical purposes. As a reasonable trade-off between realistic stylized facts, practical demands, and mathematical tractability, we propose models leading to a Markovian multi-variate survival-indicator process, and we investigate two instances of static models for the vector of default times from the statistical literature that fall into this class. On the one hand, the "looping default" case is known to be equipped with this property at least since [Herbertsson, Rootzén (2008), Bielecki et al. (2011b)], and we point out that it coincides with the classical "Freund distribution" in the bivariate case. On the other hand, if all sub-vectors of the survival indicator process are Markovian, this constitutes a new characterization of the Marshall-Olkin distribution, and hence of multi-variate lack-of-memory. A paramount property of the resulting model is stability of the type of multi-variate distribution with respect to elimination or insertion of a new marginal component with marginal distribution from the same family. The practical implications of this "nested margining" property are enormous. To implement this distribution we present an efficient and unbiased simulation algorithm based on the Lévy-frailty construction. We highlight different pitfalls in the simulation of dependent default times and examine, within a numerical case study, the effect of inadequate simulation practices.

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Section: Proofmentioning

confidence: 98%

“…The implementation of this conditional independence approach similar to Algorithm 1 is immediate. Generalizing the dependence structure to non-homogeneous structures is possible via a factor-model ansatz, see [Sun et al (2012)]. Starting from m independent Lévy subordinatorsΛ (1) , .…”

Section: Theorem 32 (Markovianity Of Survival Indicators and Lack-ofmentioning

confidence: 99%

Consistent Iterated Simulation of Multi-Variate Default Times: A Markovian Indicators Characterization

2013

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“…There exists, however, a third stochastic representation of the Marshall-Olkin distributions due to [Mai, Scherer (2009), Mai, Scherer (2011], which has been generalized and applied to portfolio-credit risk by [Sun et al (2012)]. Based on the notions of Lévy subordinators, it is called "Lévy-frailty construction", and -since it is just an alternative representation for the Marshall-Olkin law -it satisfies the practical requirements (P1) and (P2) of Section 3.…”

Section: Parameterization and Efficient Implementationmentioning

confidence: 99%

“…, d , independent of Λ, has a Marshall-Olkin distribution, cf. [Sun et al (2012), ]. Stepwise simulation is natural within this model, as Algorithm 1 shows.…”

Section: Parameterization and Efficient Implementationmentioning

confidence: 99%

Markov multi-variate survival indicators for default simulation as a new characterization of the Marshall–Olkin law

Brigo

Mai²,

Scherer

2016

Statistics & Probability Letters

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“…We perform the analysis under a cumulative default intensity model specified by a class of three-dimensional subordinators also referred to as linear factor models, see Sun et al (2014) for further details. Each coordinate of the three-dimensional subordinator consists of an idiosyncratic subordinator capturing the obligor specific risk, and of a linear combination of common subordinators modeling the systematic risk.…”

Section: Introductionmentioning

confidence: 99%

Counterparty risk for CDS: Default clustering effects

Capponi

2015

Journal of Banking & Finance

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Marshall-Olkin Multivariate Exponential Distributions, Multidimensional Subordinators, Efficient Simulation, and Applications to Credit Risk

Cited by 9 publications

References 42 publications

Consistent Iterated Simulation of Multi-Variate Default Times: A Markovian Indicators Characterization

Consistent Iterated Simulation of Multi-Variate Default Times: A Markovian Indicators Characterization

Markov multi-variate survival indicators for default simulation as a new characterization of the Marshall–Olkin law

Counterparty risk for CDS: Default clustering effects

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