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Estimation of Risk Contributions with MCMC

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  • Takaaki Koike
  • Mihoko Minami

Abstract

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 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 the consistency and asymptotic normality, and is widely applicable to various risk models having joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (approximately 500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error compared with existing estimators.

Suggested Citation

  • Takaaki Koike & Mihoko Minami, 2017. "Estimation of Risk Contributions with MCMC," Papers 1702.03098, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1702.03098
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    References listed on IDEAS

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    Cited by:

    1. Koike, Takaaki & Saporito, Yuri & Targino, Rodrigo, 2022. "Avoiding zero probability events when computing Value at Risk contributions," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 173-192.
    2. Takaaki Koike & Marius Hofert, 2020. "Modality for Scenario Analysis and Maximum Likelihood Allocation," Papers 2005.02950, arXiv.org, revised Nov 2020.
    3. Koike, Takaaki & Hofert, Marius, 2021. "Modality for scenario analysis and maximum likelihood allocation," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 24-43.
    4. Denuit, Michel & Robert, Christian Y., 2021. "Stop-loss protection for a large P2P insurance pool," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 210-233.
    5. Takaaki Koike & Marius Hofert, 2019. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Papers 1909.11794, arXiv.org, revised May 2020.
    6. Denuit, Michel & Robert, Christian Y., 2021. "Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    7. Takaaki Koike & Marius Hofert, 2020. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Risks, MDPI, vol. 8(1), pages 1-33, January.
    8. Huang, Zhenzhen & Kwok, Yue Kuen & Xu, Ziqing, 2024. "Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 132-150.

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