IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/27946.html
   My bibliography  Save this paper

From Discrete to Continuous: Modeling Volatility of the Istanbul Stock Exchange Market with GARCH and COGARCH

Author

Listed:
  • Yildirim, Yavuz
  • Unal, Gazanfer

Abstract

The objective of this paper is to model the volatility of Istanbul Stock Exchange market, ISE100 Index by ARMA and GARCH models and then take a step further into the analysis from discrete modeling to continuous modeling. Through applying unit root and stationary tests on the log return of the index, we found that log return of ISE100 data is stationary. Best candidate model chosen was found to be AR(1)~GARCH(1,1) by AIC and BIC criteria. Then using the parameters from the discrete model, COGARCH(1,1) was applied as a continuous model.

Suggested Citation

  • Yildirim, Yavuz & Unal, Gazanfer, 2010. "From Discrete to Continuous: Modeling Volatility of the Istanbul Stock Exchange Market with GARCH and COGARCH," MPRA Paper 27946, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:27946
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/27946/2/MPRA_paper_27946.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. 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.
    4. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    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. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    2. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    3. Petra Posedel, 2006. "Analysis of the Exchange Rate and Pricing Foreign Currency Options on the Croatian Market: the NGARCH Model as an Alternative to the Black-Scholes Model," Financial Theory and Practice, Institute of Public Finance, vol. 30(4), pages 347-368.
    4. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    5. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    7. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    8. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    9. Michael mcAleer, 2017. "Stationarity and Invertibility of a Dynamic Correlation Matrix," Tinbergen Institute Discussion Papers 17-082/III, Tinbergen Institute.
    10. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1291-1320, October.
    11. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    12. Christian M. Hafner & Michael McAleer, 2014. "A One Line Derivation of DCC: Application of a Vector Random Coefficient Moving Average Process," Documentos de Trabajo del ICAE 2014-29, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    13. Berkes, István & Hörmann, Siegfried & Horváth, Lajos, 2008. "The functional central limit theorem for a family of GARCH observations with applications," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2725-2730, November.
    14. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    15. 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.
    16. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Ding, Yashuang (Dexter), 2023. "A simple joint model for returns, volatility and volatility of volatility," Journal of Econometrics, Elsevier, vol. 232(2), pages 521-543.
    18. Carnero, María Ángeles, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Cassim, Lucius, 2018. "Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model," MPRA Paper 86615, University Library of Munich, Germany.
    20. Prakash L. Dheeriya & Fahimeh Rezayat & Burhan F. Yavas, 2014. "Relations between Volatility and Returns of Exchange Traded Funds of Emerging Markets and of USA," Review of Economics & Finance, Better Advances Press, Canada, vol. 4, pages 44-46, Feburary.

    More about this item

    Keywords

    ISE100; IMKB100; GARCH Modeling; COGARCH Modeling; discrete modeling; continuous modeling;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

    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:27946. 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.