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Local Estimation of Copula Based Value-at-Risk

Author

Listed:
  • Eduardo F. L. de Melo

    (Instituto de Matemática e Estatística, Universidade Estadual do Rio de Janeiro)

  • Beatriz Vaz de Melo Mendes

    (Instituto de Matemática, Universidade Federal do Rio de Janeiro)

Abstract

In this paper we propose the local maximum likelihood method for dynamically estimate copula parameters. We study the estimates statistical properties and derive the expression for their asymptotic variance in the case of Gaussian copulas. The local estimates are able to detect temporal changes in the strength of dependence among assets. These dynamics are combined with a GARCH type modeling of each individual asset to estimate the Value- at-Risk. The performance of the proposed estimates is investigated through Monte Carlo simulation experiments. In an application using real data, an out-of-sample test indicated that the new methodology may outperform the constant copula model when it comes to Value-at-Risk estimation.

Suggested Citation

  • Eduardo F. L. de Melo & Beatriz Vaz de Melo Mendes, 2009. "Local Estimation of Copula Based Value-at-Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 7(1), pages 29-50.
    • Handle: RePEc:brf:journl:v:7:y:2009:i:1:p:29-50
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    References listed on IDEAS

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    7. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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