IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/54845.html
   My bibliography  Save this paper

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]

Author

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

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).

Suggested Citation

  • Grajales Correa, Carlos Alexander & Pérez Ramírez, Fredy Ocaris & Venegas-Martínez, Francisco, 2014. "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 ," MPRA Paper 54845, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:54845
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/54845/1/MPRA_paper_54845.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. 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.
    7. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. 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.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    12. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    13. 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..
    14. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    15. Paul Wilmott & Asli Oztukel, 1998. "Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 175-189.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, March.
    4. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    5. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    6. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    7. Liu, Chang & Chang, Chuo, 2021. "Combination of transition probability distribution and stable Lorentz distribution in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    8. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    9. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    10. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    12. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    13. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    14. Pierdzioch, Christian, 2000. "Noise Traders? Trigger Rates, FX Options, and Smiles," Kiel Working Papers 970, Kiel Institute for the World Economy (IfW Kiel).
    15. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    16. Chuo Chang, 2020. "Dynamic correlations and distributions of stock returns on China's stock markets," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 10(1), pages 1-6.
    17. Schmitt, Christian, 1996. "Option pricing using EGARCH models," ZEW Discussion Papers 96-20, ZEW - Leibniz Centre for European Economic Research.
    18. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, August.
    19. Stentoft, Lars, 2011. "American option pricing with discrete and continuous time models: An empirical comparison," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 880-902.
    20. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.

    More about this item

    Keywords

    Volatilidad estocástica; heteroscedasticidad condicional; procesos de difusión; simulación Monte Carlo;
    All these keywords.

    JEL classification:

    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:54845. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.