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Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models

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  • Targino, Rodrigo S.
  • Peters, Gareth W.
  • Shevchenko, Pavel V.

Abstract

In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

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  • Targino, Rodrigo S. & Peters, Gareth W. & Shevchenko, Pavel V., 2015. "Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 206-226.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:206-226
    DOI: 10.1016/j.insmatheco.2015.01.007
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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Okhrin, Ostap & Ristig, Alexander, 2014. "Hierarchical Archimedean Copulae: The HAC Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i04).
    3. Juan-Juan Cai & John H. J. Einmahl & Laurens Haan & Chen Zhou, 2015. "Estimation of the marginal expected shortfall: the mean when a related variable is extreme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 417-442, March.
    4. Nicolas Chopin, 2002. "Central Limit Theorem for Sequential Monte Carlo Methods and its Applications to Bayesian Inference," Working Papers 2002-44, Center for Research in Economics and Statistics.
    5. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    6. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, vol. 1(1), pages 1-20, March.
    7. Walter R. Gilks & Carlo Berzuini, 2001. "Following a moving target—Monte Carlo inference for dynamic Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 127-146.
    8. Brechmann, Eike & Czado, Claudia & Paterlini, Sandra, 2014. "Flexible dependence modeling of operational risk losses and its impact on total capital requirements," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 271-285.
    9. Thomas Siller, 2013. "Measuring marginal risk contributions in credit portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1915-1923, December.
    10. Michael Kalkbrener, 2005. "An Axiomatic Approach To Capital Allocation," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 425-437, July.
    11. Philipp Arbenz & Mathieu Cambou & Marius Hofert, 2014. "An importance sampling approach for copula models in insurance," Papers 1403.4291, arXiv.org, revised Apr 2015.
    12. René Carmona & Jean-Pierre Fouque & Douglas Vestal, 2009. "Interacting particle systems for the computation of rare credit portfolio losses," Finance and Stochastics, Springer, vol. 13(4), pages 613-633, September.
    13. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    14. McLeish, Don L., 2010. "Bounded Relative Error Importance Sampling and Rare Event Simulation," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 377-398, May.
    15. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    16. Buch, A. & Dorfleitner, G., 2008. "Coherent risk measures, coherent capital allocations and the gradient allocation principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 235-242, February.
    17. Rosen, Dan & Saunders, David, 2010. "Risk factor contributions in portfolio credit risk models," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 336-349, February.
    18. Dirk Tasche, 2007. "Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle," Papers 0708.2542, arXiv.org, revised Jun 2008.
    19. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.
    20. P. Del Moral & G. W. Peters & Ch. Verg'e, 2012. "An introduction to particle integration methods: with applications to risk and insurance," Papers 1210.3851, arXiv.org, revised Oct 2012.
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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. Yuhao Liu & Petar M. Djurić & Young Shin Kim & Svetlozar T. Rachev & James Glimm, 2021. "Systemic Risk Modeling with Lévy Copulas," JRFM, MDPI, vol. 14(6), pages 1-20, June.
    3. Ignatieva, Katja & Landsman, Zinoviy, 2019. "Conditional tail risk measures for the skewed generalised hyperbolic family," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 98-114.
    4. Sunoh Kim & Jin Hur, 2020. "Probabilistic Approaches to the Security Analysis of Smart Grid with High Wind Penetration: The Case of Jeju Island’s Power Grids," Energies, MDPI, vol. 13(21), pages 1-13, November.
    5. Gareth W. Peters & Efstathios Panayi & Francois Septier, 2015. "SMC-ABC methods for the estimation of stochastic simulation models of the limit order book," Papers 1504.05806, arXiv.org.
    6. Jaume Belles-Sampera & Montserrat Guillen & Miguel Santolino, 2023. "Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem," Mathematics, MDPI, vol. 11(18), pages 1-17, September.
    7. Gareth W. Peters & Rodrigo S. Targino & Mario V. Wüthrich, 2017. "Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks," Risks, MDPI, vol. 5(4), pages 1-51, September.
    8. Ji, Liuyan & Tan, Ken Seng & Yang, Fan, 2021. "Tail dependence and heavy tailedness in extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 282-293.
    9. Takaaki Koike & Marius Hofert, 2019. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Papers 1909.11794, arXiv.org, revised May 2020.
    10. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    11. Takaaki Koike & Marius Hofert, 2020. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Risks, MDPI, vol. 8(1), pages 1-33, January.
    12. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    13. Mélina Mailhot & Mhamed Mesfioui, 2016. "Multivariate TVaR-Based Risk Decomposition for Vector-Valued Portfolios," Risks, MDPI, vol. 4(4), pages 1-16, September.

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    More about this item

    Keywords

    Risk management; Capital allocation; Sequential Monte Carlo (SMC); Copula models; Euler allocation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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