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Article: Markov chain monte carlo methods for estimating systemic risk allocations

TitleMarkov chain monte carlo methods for estimating systemic risk allocations
Authors
KeywordsCapital allocation
Conditional Value-at-Risk (CoVaR)
Copula models
Quantitative risk management
Systemic risk measures
Issue Date2020
Citation
Risks, 2020, v. 8, n. 1, article no. 6 How to Cite?
AbstractIn this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.
Persistent Identifierhttp://hdl.handle.net/10722/325467
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorKoike, Takaaki-
dc.contributor.authorHofert, Marius-
dc.date.accessioned2023-02-27T07:33:33Z-
dc.date.available2023-02-27T07:33:33Z-
dc.date.issued2020-
dc.identifier.citationRisks, 2020, v. 8, n. 1, article no. 6-
dc.identifier.urihttp://hdl.handle.net/10722/325467-
dc.description.abstractIn this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.-
dc.languageeng-
dc.relation.ispartofRisks-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectCapital allocation-
dc.subjectConditional Value-at-Risk (CoVaR)-
dc.subjectCopula models-
dc.subjectQuantitative risk management-
dc.subjectSystemic risk measures-
dc.titleMarkov chain monte carlo methods for estimating systemic risk allocations-
dc.typeArticle-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.3390/risks8010006-
dc.identifier.scopuseid_2-s2.0-85079478620-
dc.identifier.volume8-
dc.identifier.issue1-
dc.identifier.spagearticle no. 6-
dc.identifier.epagearticle no. 6-
dc.identifier.eissn2227-9091-
dc.identifier.isiWOS:000524496300018-

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