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Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations

Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
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Received: 24 September 2019 / Revised: 2 January 2020 / Accepted: 7 January 2020 / Published: 15 January 2020
(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)
In 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. View Full-Text
Keywords: systemic risk measures; conditional Value-at-Risk (CoVaR); capital allocation; copula models; quantitative risk management systemic risk measures; conditional Value-at-Risk (CoVaR); capital allocation; copula models; quantitative risk management
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MDPI and ACS Style

Koike, T.; Hofert, M. Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations. Risks 2020, 8, 6. https://doi.org/10.3390/risks8010006

AMA Style

Koike T, Hofert M. Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations. Risks. 2020; 8(1):6. https://doi.org/10.3390/risks8010006

Chicago/Turabian Style

Koike, Takaaki, and Marius Hofert. 2020. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations" Risks 8, no. 1: 6. https://doi.org/10.3390/risks8010006

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