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Volatility Estimation via Hidden Markov Models

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Abstract

In this paper we suggest a convenient way to obtain parameter estimates of a discrete state hidden Markov volatility process within a framework consistent with observed option prices and stochastic volatility. Relative to similar proposals, we simplify the model estimation by resorting to some parametric approximation of the model in a maximum likelihood context. We show how correlation between returns and volatility innovations can be easily accommodated within this framework. Empirical applications illustrate model search strategies for the SP500 stock index, comparing the performances to a standard GARCH model.

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  • Alessandro Rossi & Giampiero M. Gallo, 2002. "Volatility Estimation via Hidden Markov Models," Econometrics Working Papers Archive wp2002_14, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2002_14
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    Cited by:

    1. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
    2. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    3. Fulvia Pennoni & Francesco Bartolucci & Gianfranco Forte & Ferdinando Ametrano, 2022. "Exploring the dependencies among main cryptocurrency log‐returns: A hidden Markov model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(1), February.
    4. repec:onb:oenbwp:y:2010:i:2:b:1 is not listed on IDEAS
    5. Markus Eller & Michael Frömmel & Nora Srzentic, 2010. "Private Sector Credit in CESEE: Long-Run Relationships and Short-Run Dynamics," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 2, pages 50-78.
    6. AUGUSTYNIAK, Maciej & BAUWENS, Luc & DUFAYS, Arnaud, 2016. "A New Approach to Volatility Modeling : The High-Dimensional Markov Model," LIDAM Discussion Papers CORE 2016042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Hugh Christensen & Simon Godsill & Richard E Turner, 2020. "Hidden Markov Models Applied To Intraday Momentum Trading With Side Information," Papers 2006.08307, arXiv.org.
    8. Michael Frömmel, 2010. "Volatility Regimes in Central and Eastern European Countries’ Exchange Rates," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 60(1), pages 2-21, February.
    9. Luca De Angelis & Leonard J. Paas, 2013. "A dynamic analysis of stock markets using a hidden Markov model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1682-1700, August.
    10. Lux, Thomas & Morales-Arias, Leonardo, 2009. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Kiel Working Papers 1532, Kiel Institute for the World Economy (IfW Kiel).
    11. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    12. Lux, Thomas & Morales-Arias, Leonardo & Sattarhoff, Cristina, 2011. "A Markov-switching multifractal approach to forecasting realized volatility," Kiel Working Papers 1737, Kiel Institute for the World Economy (IfW Kiel).
    13. L. Grossi & G. Morelli, 2006. "Robust volatility forecasts and model selection in financial time series," Economics Department Working Papers 2006-SE02, Department of Economics, Parma University (Italy).
    14. Carlos A. Abanto‐Valle & Roland Langrock & Ming‐Hui Chen & Michel V. Cardoso, 2017. "Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(4), pages 394-408, August.
    15. Xun Huang & Huiyue Tang, 2022. "Measuring multi‐volatility states of financial markets based on multifractal clustering model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 422-434, April.
    16. Dias, José G. & Vermunt, Jeroen K. & Ramos, Sofia, 2015. "Clustering financial time series: New insights from an extended hidden Markov model," European Journal of Operational Research, Elsevier, vol. 243(3), pages 852-864.
    17. Langrock, Roland & MacDonald, Iain L. & Zucchini, Walter, 2012. "Some nonstandard stochastic volatility models and their estimation using structured hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 19(1), pages 147-161.
    18. Francesco Bartolucci & Silvia Bacci & Fulvia Pennoni, 2014. "Longitudinal analysis of self-reported health status by mixture latent auto-regressive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 267-288, February.

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    More about this item

    Keywords

    Stochastic volatility; Hidden Markov; GARCH; Smile-consistent option pricing; Forecasting.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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