TY - JOUR
T1 - Estimation of risk contributions with MCMC
AU - Koike, Takaaki
AU - Minami, Mihoko
N1 - Funding Information:
This work was supported by the Japan Society for the Promotion of Science (JSPS) under the Core-to-Core program at Keio University. We wish to thank to Paul Embrechts from ETH Z?rich for his valuable comments regarding the simulation setup. We would also like to express our gratitude to Kengo Kamatani from Osaka University, and Marius Hofert from the University of Waterloo for fruitful discussions on MCMC and Archimedean copulas. Finally, we are thankful to an associate editor and anonymous referees for their careful reading of the manuscript and their insightful comments.
Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019
Y1 - 2019
N2 - Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we address the problem of estimating risk contributions when the total risk is measured by value-at-risk (VaR). Our proposed estimator of VaR contributions is based on the Metropolis-Hasting (MH) algorithm, which is one of the most prevalent Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MH-based estimator consists of samples from the conditional loss distribution given a rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method. Moreover, our method has consistency and asymptotic normality, and is widely applicable to various risk models having a joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (≈500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error when compared with existing estimators.
AB - Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we address the problem of estimating risk contributions when the total risk is measured by value-at-risk (VaR). Our proposed estimator of VaR contributions is based on the Metropolis-Hasting (MH) algorithm, which is one of the most prevalent Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MH-based estimator consists of samples from the conditional loss distribution given a rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method. Moreover, our method has consistency and asymptotic normality, and is widely applicable to various risk models having a joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (≈500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error when compared with existing estimators.
KW - Copulas
KW - Markov chain Monte Carlo
KW - Metropolis-Hastings algorithm
KW - Risk allocation
KW - Risk contributions
KW - VaR contributions
KW - Value-at-risk
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U2 - 10.1080/14697688.2019.1588469
DO - 10.1080/14697688.2019.1588469
M3 - Article
AN - SCOPUS:85064638789
VL - 19
SP - 1579
EP - 1597
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
IS - 9
ER -