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Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review

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  • Degiannakis, Stavros
  • Xekalaki, Evdokia

Abstract

Autoregressive Conditional Heteroscedasticity (ARCH) models have successfully been employed in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of univariate and multivariate ARCH models, their estimating methods and the characteristics of financial time series, which are captured by volatility models, are presented. The number of possible conditional volatility formulations is vast. Therefore, a systematic presentation of the models that have been considered in the ARCH literature can be useful in guiding one’s choice of a model for exploiting future volatility, with applications in financial markets.

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  • Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:80487
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    Cited by:

    1. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    2. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    3. Timotheos Angelidis & Stavros Degiannakis, 2005. "Modeling risk for long and short trading positions," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 6(3), pages 226-238, July.
    4. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Assessing the performance of a prediction error criterion model selection algorithm in the context of ARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 17(2), pages 149-171.
    5. Stavros Degiannakis & Evdokia Xekalaki, 2007. "Simulated evidence on the distribution of the standardized one-step-ahead prediction errors in ARCH processes," Applied Financial Economics Letters, Taylor & Francis Journals, vol. 3(1), pages 31-37.
    6. Willy Alanya & Gabriel Rodríguez, 2019. "Asymmetries in Volatility: An Empirical Study for the Peruvian Stock and Forex Markets," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-18, March.
    7. Uctum, Remzi & Renou-Maissant, Patricia & Prat, Georges & Lecarpentier-Moyal, Sylvie, 2017. "Persistence of announcement effects on the intraday volatility of stock returns: Evidence from individual data," Review of Financial Economics, Elsevier, vol. 35(C), pages 43-56.
    8. Wen Cheong, Chin & Hassan Shaari Mohd Nor, Abu & Isa, Zaidi, 2007. "Asymmetry and long-memory volatility: Some empirical evidence using GARCH," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 651-664.
    9. Willy Alanya & Gabriel Rodríguez, 2018. "Stochastic Volatility in the Peruvian Stock Market and Exchange Rate Returns: A Bayesian Approximation," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 17(3), pages 354-385, December.
    10. repec:ipg:wpaper:27 is not listed on IDEAS
    11. Stavros Degiannakis & Evdokia Xekalaki, 2005. "Predictability and model selection in the context of ARCH models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 21(1), pages 55-82, January.
    12. Stavros Degiannakis, 2004. "Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model," Applied Financial Economics, Taylor & Francis Journals, vol. 14(18), pages 1333-1342.
    13. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    14. Saker Sabkha & Christian de Peretti, 2018. "On the performances of Dynamic Conditional Correlation models in the Sovereign CDS market and the corresponding bond market," Working Papers hal-01710398, HAL.
    15. Emenike, Kalu O., 2018. "Stock Market Volatility Clustering and Asymmetry in Africa: A Post Global Financial Crisis Evidence," MPRA Paper 91653, University Library of Munich, Germany.
    16. Degiannakis, Stavros, 2004. "Forecasting Realized Intra-day Volatility and Value at Risk: Evidence from a Fractional Integrated Asymmetric Power ARCH Skewed-t Model," MPRA Paper 80488, University Library of Munich, Germany.
    17. Angelidis, Timotheos & Benos, Alexandros & Degiannakis, Stavros, 2004. "The Use of GARCH Models in VaR Estimation," MPRA Paper 96332, University Library of Munich, Germany.
    18. repec:ipg:wpaper:2013-027 is not listed on IDEAS
    19. Twm Evans & David McMillan, 2007. "Volatility forecasts: the role of asymmetric and long-memory dynamics and regional evidence," Applied Financial Economics, Taylor & Francis Journals, vol. 17(17), pages 1421-1430.
    20. Saker Sabkha & Christian de Peretti, 2022. "On the performances of Dynamic Conditional Correlation models in the Sovereign CDS market and the corresponding bond market," Post-Print hal-01710398, HAL.
    21. Maghyereh Aktham Issa & Awartani Basel, 2012. "Modeling and Forecasting Value-at-Risk in the UAE Stock Markets: The Role of Long Memory, Fat Tails and Asymmetries in Return Innovations," Review of Middle East Economics and Finance, De Gruyter, vol. 8(1), pages 1-22, August.
    22. Sylvie Lecarpentier-Moyal & Georges Prat & Patricia Renou-Maissant & Remzi Uctum, 2013. "Persistence of announcement effects on the intraday volatility of stock returns: evidence from individual data," Working Papers hal-04141172, HAL.
    23. Hashem Zarafat & Sascha Liebhardt & Mustafa Hakan Eratalay, 2022. "Do ESG Ratings Reduce the Asymmetry Behavior in Volatility?," JRFM, MDPI, vol. 15(8), pages 1-32, July.

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    More about this item

    Keywords

    ARCH models; Forecast Volatility.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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