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Estimación del VaR mediante un modelo condicional multivariado bajo la hipótesis α-estable sub-Gaussiana

Author

Listed:
  • Ramona Serrano-Bautista

    (Tecnológico de Monterrey)

  • Leovardo Mata-Mata

    (Tecnológico de Monterrey.)

Abstract

El objetivo de esta investigación es proponer un modelo de volatilidad multivariable, el cual combina la propiedad de la distribución α-estable para ajustar colas pesadas con el modelo GARCH para capturar clúster de volatilidad. El supuesto inicial es que los rendimientos siguen una distribución sub-Gaussiana, la cual es un caso particular de las distribuciones estables multivariadas. El modelo GARCH propuesto se aplica en la estimación del VaR a un portafolio compuesto por cinco activos que cotizan en la Bolsa Mexicana de Valores (BMV). En particular, se compara el desempeño del modelo propuesto con la estimación del VaR obtenida bajo la hipótesis multivariada Gaussiana, t-Student y Cauchy durante el período de la crisis financiera de 2008.

Suggested Citation

  • Ramona Serrano-Bautista & Leovardo Mata-Mata, 2018. "Estimación del VaR mediante un modelo condicional multivariado bajo la hipótesis α-estable sub-Gaussiana," Ensayos Revista de Economía, Universidad Autónoma de Nuevo León, vol. 37(1), pages 43-76, April.
  • Handle: RePEc:ere:journl:v:37:y:2018:i:1:id:121
    DOI: 10.29105/ensayos37.1-2
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    References listed on IDEAS

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    1. B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153, April.
    2. Ramona Serrano Bautista & Leovardo Mata Mata, 2018. "Valor en Riesgo mediante un modelo heterocedástico condicional ?-estable," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 13(1), pages 1-26, Enero-Mar.
    3. Mohammad Mohammadi, 2017. "Prediction of α ‐stable GARCH and ARMA‐GARCH‐M models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(7), pages 859-866, November.
    4. Byczkowski, T. & Nolan, J. P. & Rajput, B., 1993. "Approximation of Multidimensional Stable Densities," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 13-31, July.
    5. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    6. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. J. Huston McCulloch, 2000. "Estimation of the Bivariate Stable Spectral Representation by the Projection Method," Computational Economics, Springer;Society for Computational Economics, vol. 16(1/2), pages 47-62, October.
    9. Svetlozar Rachev & Seonkoo Han, 2000. "Portfolio management with stable distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 341-352, April.
    10. John P. Nolan, 2001. "Maximum Likelihood Estimation and Diagnostics for Stable Distributions," Springer Books, in: Ole E. Barndorff-Nielsen & Sidney I. Resnick & Thomas Mikosch (ed.), Lévy Processes, pages 379-400, Springer.
    11. Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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