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Análisis comparativo de modelos para estimar la distribución de la volatilidad de series financieras de rendimientos
[A Comparative Analysis of Models for Estimating the Volatility Distribution of Financial Returns Series]

  • Grajales Correa, Carlos Alexander
  • Pérez Ramírez, Fredy Ocaris
  • Venegas-Martínez, Francisco

Spanish Abstract: En este trabajo se presenta un marco teórico que conjunta y ordena sistemáticamente, en cuanto a complejidad y realismo, varios modelos disponibles en la literatura especializada para estimar la distribución de la volatilidad de los rendimientos diarios de índices bursátiles. Para tal fin se consideran los modelos discretos ARCH y algunas de sus extensiones, así como los modelos de difusión en tiempo continuo. En el caso discreto, los modelos estiman la volatilidad por medio de la heteroscedasticidad condicional. Mientras que en el caso continuo, los modelos estiman la distribución de la volatilidad a través de procesos estocásticos de difusión, en cuyo caso se utiliza simulación Monte Carlo. Por último se comparan los resultados obtenidos con las diferentes metodologías para los índices bursátiles: S&P 500 de EEUU, Índice de Precios y Cotizaciones de la Bolsa Mexicana de Valores (IPC) e Índice General de la Bolsa de Valores de Colombia (IGBC). English Abstract: This aim of this paper is to present a theoretical framework that systematically joint and ordered, according to realism and complexity, several available models in the specialized literature useful to estimate the volatility distribution of stock indices. To this end, discrete ARCH models and some of its extensions, as well as continuous time diffusion models are considered. In the discrete case, the models estimate volatility from the conditional heteroscedasticity. Meanwhile, in the continuous case, the models estimate the volatility distribution through diffusion stochastic processes, which allows using Monte Carlo simulation. Finally, the obtained results from the different methodologies are compared for the capital stock indices: S &P 500 of the U. S. A. , Index of Prices of the Mexican Stock Market (IPC), and the General Index of Prices of the Colombian Stock Market (IGBC).

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 54845.

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Date of creation: 28 Mar 2014
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Handle: RePEc:pra:mprapa:54845
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  1. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
  2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
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  9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  10. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  11. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  13. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  14. 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.
  15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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