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Dynamic D-Vine copula model with applications to Value-at-Risk (VaR)

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  • Tófoli, Paula Virgínia
  • Ziegelmann, Flávio Augusto
  • Silva Filho, Osvaldo Candido
  • Pereira, Pedro L. Valls

Abstract

Regular vine copulas are multivariate dependence models constructed from pair-copulas (bivariate copulas). In this paper, we allow the dependence parameters of the pair-copulas in a D-vine decomposition to be potentially time-varying, following a nonlinear restricted ARMA(1,m) process, in order to obtain a very flexible dependence model for applications to multivariate financial return data. We investigate the dependence among the broad stock market indexes from Germany (DAX), France (CAC 40), Britain (FTSE 100), the United States (S&P 500) and Brazil (IBOVESPA) both in a crisis and in a non-crisis period. We find evidence of stronger dependence among the indexes in bear markets. Surprisingly, though, the dynamic D-vine copula indicates the occurrence of a sharp decrease in dependence between the indexes FTSE and CAC in the beginning of 2011, and also between CAC and DAX during mid-2011 and in the beginning of 2008, suggesting the absence of contagion in these cases. We also evaluate the dynamic D-vine copula with respect to Value-at-Risk (VaR) forecasting accuracy in crisis periods. The dynamic D-vine outperforms the static D-vine in terms of predictive accuracy for our real data sets.

Suggested Citation

  • Tófoli, Paula Virgínia & Ziegelmann, Flávio Augusto & Silva Filho, Osvaldo Candido & Pereira, Pedro L. Valls, 2016. "Dynamic D-Vine copula model with applications to Value-at-Risk (VaR)," Textos para discussão 424, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    • Handle: RePEc:fgv:eesptd:424
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    1. Sabino da Silva, Fernando A.B. & Ziegelmann, Flavio A. & Caldeira, João F., 2023. "A pairs trading strategy based on mixed copulas," The Quarterly Review of Economics and Finance, Elsevier, vol. 87(C), pages 16-34.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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