Grajales Correa, Carlos Alexander and Pérez Ramírez, Fredy Ocaris and Venegas-Martínez, Francisco (2014): Análisis comparativo de modelos para estimar la distribución de la volatilidad de series financieras de rendimientos.
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Abstract
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).
Item Type: | MPRA Paper |
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Original Title: | Análisis comparativo de modelos para estimar la distribución de la volatilidad de series financieras de rendimientos |
English Title: | A Comparative Analysis of Models for Estimating the Volatility Distribution of Financial Returns Series |
Language: | Spanish |
Keywords: | Volatilidad estocástica, heteroscedasticidad condicional, procesos de difusión, simulación Monte Carlo |
Subjects: | G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation |
Item ID: | 54845 |
Depositing User: | Dr. Francisco Venegas-Martínez |
Date Deposited: | 08 Apr 2014 11:29 |
Last Modified: | 28 Sep 2019 17:28 |
References: | Oztukel, A, and P. Wilmott (1998). Uncertain Parameters: An Empirical Stochastic Volatility Model and Confidence Limits. International Journal of Theoretical and Applied Finance, Vol. 1, No. 1, pp. 175-189. Baillie, R. T, T. Bollerslev, and H. O. Mikkelsen (1996). Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, Vol. 74, No. 1, pp. 3-30. Black, F. and M. Scholes (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, Vol. 81, No. 3, pp. 637-654. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, Vol. 31, pp. 307-327. Derman, E and I. Kani (1994). Riding on a Smile. Risk, Vol. 7, No. 2, pp. 32-39. Doran, J. S. and E. I. Ronn (2004). On the Market Price of Volatility Risk. Florida State University and University of Texas at Austin. Dupire, B. (1994). Pricing on a Smile, Risk, Vol. 7, No. 1, pp. 18-20. Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflations. Econometrica, Vol. 50, pp. 987-1008. Fama, E. (1965). The Behaviour of Stock Price. Journal of Business, Vol. 38, pp. 34-105. Heston, S. I. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, Vol. 6, No. 2, pp. 327-343. Hull, J. and A. White, 1987. The Pricing of Options on Assets with Stochastic Volatility. Journal of Finance, Vol. 42, No. 2, pp. 281-300. Hull, C. John, (2005). Options Futures and Other Derivatives. 6th ed. Englewood Cliffs, N. J., Prentice-Hall. Kloeden, P. and E. Platen (1992). Numerical Solution of Stochastic Differential Equations. Springer-Verlag. Deakin University, Australian National University, Australia. Mandelbrot, B. (1963). The Variation of Certain Speculative Prices. Journal of Business, 36, 394–419. Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics, Vol.4, No. 1, pp. 141-183. Nelson, D. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, Vol. 59, pp. 347-370. Robinson, P. M. (1991). Testing for Strong Serial Correlation and Dynamic Conditional Heteroskedasticity in Multiple Regression. Journal of Econometrics, Vol. 47, pp. 67-84. Rubinstein, M. (1994). Implied Binomial Trees. Journal of Finance, Vol. 49, No. 3, pp. 771-818. Scott, L. O. (1987). Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application. The Journal of Financial and Quantitative Analysis, Vol. 22, No. 4, pp. 419-438. Stein, E. M. and Stein, J. C. (1991). Stock Price Distributions with Stochastic Volatility: An Analytic Approach. The Review of Financial Studies, Vol. 4, No. 4, pp. 727-752. Tsay, R. (2005). Analysis of Financial Time Series. John Wiley & Sons. Second Edition. Wiggins, J. B. (1987). Option Values under Stochastic Volatility: Theory and Empirical Estimates. Journal of Financial and Quantitative Analysis, Vol. 19, pp. 351-372. Wilmott, P. (1998). Derivatives. The Theory and Practice of Financial Engineering. John Wiley & Sons, England. Wilmott, P. (2000). Paul Wilmott on Quantitative Finance. Volume one. John Wiley & Sons, England. Zakoian, J. (1994). Threshold Heteroskedastic Models. Journal of Economic Dynamics and Control, Vol. 18, pp. 931-944. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/54845 |