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Extreme Value Theory: An Application to the Peruvian Stock Market Returns

Author

Listed:
  • Alfredo Calderon Vela

    ( Departamento de Economía - Pontificia Universidad Católica del Perú)

  • Gabriel Rodríguez

    ( Departamento de Economía - Pontificia Universidad Católica del Perú)

Abstract

Using daily observations of the index and stock market returns for the Peruvian case from January 3, 1990 to May 31, 2013, this paper models the distribution of daily loss probability, estimates maximum quantiles and tail probabilities of this distribution, and models the extremes through a maximum threshold. This is used to obtain the better measurements of the Value at Risk (VaR) and the Expected Short-Fall (ES) at 95% and 99%. One of the results on calculating the maximum annual block of the negative stock market returns is the observation that the largest negative stock market return (daily) is 12.44% in 2011. The shape parameter is equal to -0.020 and 0.268 for the annual and quarterly block, respectively. Then, in the Örst case we have that the non-degenerate distribution function is Gumbel-type. In the other case, we have a thick-tailed distribution (FrÈchet). Estimated values of the VaR and the ES are higher using the Generalized Pareto Distribution (GPD) in comparison with the Normal distribution and the di§erences at 99.0% are notable. Finally, the non-parametric estimation of the Hill tail-index and the quantile for negative stock market returns shows quite instability. JEL Classification-JEL: C22, C58, G32.

Suggested Citation

  • Alfredo Calderon Vela & Gabriel Rodríguez, 2014. "Extreme Value Theory: An Application to the Peruvian Stock Market Returns," Documentos de Trabajo / Working Papers 2014-394, Departamento de Economía - Pontificia Universidad Católica del Perú.
    • Handle: RePEc:pcp:pucwps:wp00394
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    File URL: http://files.pucp.edu.pe/departamento/economia/DDD394.pdf
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    References listed on IDEAS

    as
    1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 2000. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 1(2), pages 30-35, January.
    2. Humala, Alberto & Rodriguez, Gabriel, 2010. "Some stylized facts of returns in the foreign exchange and stock markets in Peru," Working Papers 2010-017, Banco Central de Reserva del Perú.
    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    4. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    5. Alberto Humala & Gabriel Rodriguez, 2013. "Some stylized facts of return in the foreign exchange and stock markets in Peru," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 30(2), pages 139-158, May.
    6. Miguel T. Delfiner & Matías A. Gutiérrez Girault, 2002. "Aplicación de la teoría de valores extremos al gerenciamiento del riesgo," CEMA Working Papers: Serie Documentos de Trabajo. 217, Universidad del CEMA.
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    More about this item

    Keywords

    Extreme Value Theory; Value-at-Risk (VaR); Expected Short-Fall (ES); Generalized Pareto Distribution (GPD); Distributions Gumbel; Exponential; FrÈchet; Extreme Loss; Peruvian Stock Market.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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