Estimación del VaR mediante un modelo condicional multivariado bajo la hipótesis α-estable sub-Gaussiana
A conditional approach to VaR with multivariate α-stable sub-Gaussian distributions
DOI:
https://doi.org/10.29105/ensayos37.1-2Palabras clave:
Distribución α-estable Sub-Gaussiana, GARCH multivariado estable Sub-Gaussiano, Valor en RiesgoResumen
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.
Descargas
Citas
Barndorff-Nielsen, O.E., Mikosch, T. y Resnick, S.I. (2012). Lévy Processes: Theory and Applications, Springer Science & Business Media, New York, NY.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.
Bonato, M. (2012). Modeling fat tails in stock returns: A multivariate stable-GARCH approach. Computational Statistics, 27(3), 499–521.
Byczkowski, T., Nolan, J.P. y Rajput, B. (1993). Approximation of Multidimensional Stable Densities. Journal of Multivariate Analysis, 46(1), 13–31. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0047259X83710444.
Cheng, B., y Rachev, S. (1995). Multivariate stable futures prices. Journal of Mathematical Finance, 5, 133-153.
Curto, J.D., Pinto, J.C. y Tavares, G.N. (2009). Modeling stock markets’ volatility using GARCH models with Normal, Student’s t and stable Paretian distributions. Statistical Papers, 50(2), 311–321.
Engle, R.F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometría, 50(4), 987–1007.
Engle, R. (2002). Dynamic Conditional Correlation. Journal of Business & Economic Statistics, 20(3), 339–350. Available at: http://www.tandfonline.com/doi/abs/10.1198/073500102288618487#.VyvCUaCAdvE.mendeley.
Fama, E.F. (1965). The Behavior of Stock-Market Prices. The Journal of Business, 38(1), 34–105.
Feldheim, E. (1937). Etude de la stabilité des lois de probabilité. Ph. D. thesis, Faculté des Sciences de Paris, Paris, France.
Khindanova, I., Rachev, S. y Schwartz, E. (2001). Stable Modeling of Value at Risk. Mathematical and Computer Modelling, 34, 1223–1259.
Kring, S., Rachev, S., Markus, H. y Fabozzi, F. (2009). Estimation of α-Stable Sub-Gaussian Distributions.pdf. In Risk Assessment Decisions in Banking and FinanceDecisions in Banking and Finance. 111–152.
Kupiec, P.H. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 3(2), 73-84.
Mandelbrot. (1963). The variation of certain speculative prices. The Journal of Business, 36, 394–419.
McCulloch, J.H. (1986). Simple consistent estimators of stable distribution parameters. Communications in Statistics - Simulation and Computation, 15, 1109–1136.
Mcculloch, J.H. (2000). Estimation of the Bivariate Stable Spectral Representation by the Projection Method. Computational Economics, 16(1–2), 47–62.
Mittnik, S., Doganoglu, T. y Chenyao, D. (1999). Computing the probability density function of the stable Paretian distribution. Mathematical and Computer Modelling, 29(10–12), 235–240.
Mittnik, S., Paolella, M.S. y Rachev, S.T. (2002). Stationarity of stable power-GARCH processes. Journal of Econometrics, 106, 97–107.
Mittnik, S. y Rachev, S.T. (1989). Stable distributions for asset returns. Applied Mathematics Letters, 2(3), 301–304.
Mittnik, S. y Rachev, S.T. (1993). Modeling asset returns with alternative stable distributions. Economics Reviews, 12, 261–330.
Mittnik, S., Rachev S., y Paolella, M. (1997). Stable Paretian Modelling in Finance: Some Empirical and Theorical Aspects, in R. Adler, R. E. Feldman and M.S. Taqqu (eds).
Modarres, R., y Nolan, J.P. (1994). A method for simulating stable random vectors. Computational Statistics, 9, 11-19.
Mohammadi, M. (2017). Prediction of -stable GARCH and ARMA-GARCH-M models. Journal of Forecasting, 36, 859–866.
Naka, A. y Oral, E. (2013). With Stable Paretian GARCH. Journal of Business & Economics Research, 11(1), 47–53.
Nolan, J.P. (1997). Numerical calculation of stable densities and distribution functions. Commun. Statist. Stochastic Models, 13, 759-774.
Nolan, J. (1999). Fitting data and assessing goodness-of-fit with stable distributions. Unpublished Manuscript. Washington, DC, 2(1924). Available at: http://academic2.american.edu/~jpnolan/stable/DataAnalysis.pdf.
Nolan, J.P. (2001). Maximum Likelihood Estimation and Diagnostics for Stable Distributions. , (January 2001). Available at: http://link.springer.com/10.1007/978-1-4612-0197-7.
Nolan, J.P. (2013). Multivariate elliptically contoured stable distributions: Theory and estimation. Computational Statistics, 28(5), 2067–2089.
Nolan, J.P., Panorska, A.K. y McCulloch, J.H. (2001). Estimation of stable spectral measures. Mathematical and Computer Modelling, 34(9–11), 1113–1122.
Nolan, J.P., y Rajput, B. (1997). Calculation of multidimensional stable densities. Commun. Statist. Simula, 24, 551-556.
Panorska, A., Mittnik, S., and Rachev, S.T., 1995. Stable GARCH Models for Financial Time Series. Applied Mathematics Letters, 8(5), 33–37.
Press, S.J., (1972). Estimation in Univariate and Multivariate Stable Distributions. Journal of the American Statistical Association, 67(340), 842–846.
Rachev, S.T, y Mittnik, S., (2000). Stable Paretian Models in Finance. New York, NY: Wiley.
Rachev, S. y Han, S., (2000). Portfolio management with stable distributions. Mathematical Methods of Operation Research, 51, 341–352.
Samorodnitsky, G., y Taqqu, M., 1994. Stable Non-Gaussian Random Processes. New York: Chapman and Hall.
Serrano y Mata, (2018). Valor en Riesgo mediante un modelo heterocedástico condicional α-estable. REMEF, 13(1), 1-25.
Publicado
Cómo citar
Número
Sección
Licencia
Derechos de autor 2018 Ramona Serrano-Bautista, Leovardo Mata-Mata
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
