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Estimation of VaR Using Copula and Extreme Value Theory

Author

Listed:
  • L. K. Hotta

    (State University of Campinas, Campinas SP, Brazil)

  • E. C. Lucas

    (ESAMC, Campinas SP, Brazil)

  • H. P Palaro

    (State University of Campinas, Campinas SP, Brazil and Cass Business School, U.K.)

Abstract

This paper proposes a method for estimating the VaR of a portfolio based on copula and extreme value theory. Each return is modeled by ARMA-GARCH models with the joint distribution of innovations modeled by copula. The marginal distributions are modeled by the generalized Pareto distribution in the left tail (large loss) and empirical distribution otherwise. The copula is estimated by an estimator which gives more weight to observations with large loss. The method is applied to a two-asset portfolio and compared to other traditional methods.

Suggested Citation

  • L. K. Hotta & E. C. Lucas & H. P Palaro, 2008. "Estimation of VaR Using Copula and Extreme Value Theory," Multinational Finance Journal, Multinational Finance Journal, vol. 12(3-4), pages 205-218, September.
    • Handle: RePEc:mfj:journl:v:12:y:2008:i:3-4:p:205-218
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    References listed on IDEAS

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    Cited by:

    1. Junni L. Zhang & Wolfgang Karl Hardle & Cathy Y. Chen & Elisabeth Bommes, 2020. "Distillation of News Flow into Analysis of Stock Reactions," Papers 2009.10392, arXiv.org.
    2. Chun-Pin Hsu & Chin-Wen Huang & Wan-Jiun Chiou, 2012. "Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 447-468, November.
    3. Karmakar, Madhusudan, 2017. "Dependence structure and portfolio risk in Indian foreign exchange market: A GARCH-EVT-Copula approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 275-291.
    4. Ghorbel, Ahmed & Trabelsi, Abdelwahed, 2014. "Energy portfolio risk management using time-varying extreme value copula methods," Economic Modelling, Elsevier, vol. 38(C), pages 470-485.
    5. Mirela NICHITA, 2015. "An Overview On State Of Knowledge Of Risk And Risk Management In Economics Fields," SEA - Practical Application of Science, Romanian Foundation for Business Intelligence, Editorial Department, issue 7, pages 423-430, April.
    6. Anderson Ara & Francisco Louzada & Carlos A. R. Diniz, 2017. "Statistical monitoring of a web server for error rates: a bivariate time-series copula-based modeling approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2287-2300, October.
    7. Duy Duong & Toan Luu Duc Huynh, 2020. "Tail dependence in emerging ASEAN-6 equity markets: empirical evidence from quantitative approaches," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-26, December.
    8. Kellner, Ralf & Gatzert, Nadine, 2013. "Estimating the basis risk of index-linked hedging strategies using multivariate extreme value theory," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4353-4367.
    9. Huang, Jen-Jsung & Lee, Kuo-Jung & Liang, Hueimei & Lin, Wei-Fu, 2009. "Estimating value at risk of portfolio by conditional copula-GARCH method," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 315-324, December.
    10. Nader Trabelsi & Aviral Kumar Tiwari, 2019. "Market-Risk Optimization among the Developed and Emerging Markets with CVaR Measure and Copula Simulation," Risks, MDPI, vol. 7(3), pages 1-20, July.
    11. Beatriz de la Flor & Javier Ojea-Ferreiro & Eva Ferreira, 2022. "The Hedging Cost of Forgetting the Exchange Rate," Documentos de Trabajo del ICAE 2022-01, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    12. Alexandru Stanga, 2008. "Measuring market risk: a copula and extreme value approach," Advances in Economic and Financial Research - DOFIN Working Paper Series 13, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.

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    More about this item

    Keywords

    conditional copula; risk measures; VaR; extreme value theory;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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