IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v13y2006i2p203-230.html
   My bibliography  Save this article

Volatility estimation via hidden Markov models

Author

Listed:
  • Rossi, Alessandro
  • Gallo, Giampiero M.

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    • Handle: RePEc:eee:empfin:v:13:y:2006:i:2:p:203-230
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927-5398(05)00075-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    4. West, Kenneth D. & Cho, Dongchul, 1995. "The predictive ability of several models of exchange rate volatility," Journal of Econometrics, Elsevier, vol. 69(2), pages 367-391, October.
    5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    6. Jin-Chuan Duan & Ivilina Popova & Peter Ritchken, 2002. "Option pricing under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 116-132.
    7. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    8. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    10. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    11. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    12. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    13. Martin D. D. Evans, 2003. "Real risk, inflation risk, and the term structure," Economic Journal, Royal Economic Society, vol. 113(487), pages 345-389, April.
    14. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    15. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.
    16. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    17. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-229, March.
    18. Andrew C. Harvey, 1990. "The Econometric Analysis of Time Series, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026208189x, April.
    19. Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 49-83.
    20. Elliott, Robert J. & Hunter, William C. & Jamieson, Barbara M., 1998. "Drift and volatility estimation in discrete time," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 209-218, February.
    21. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    22. Benjamin M. Friedman & David I. Laibson, 1989. "Economic Implications of Extraordinary Movements in Stock Prices," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(2), pages 137-190.
    23. Maravall, Agustin & Planas, Christophe, 1999. "Estimation error and the specification of unobserved component models," Journal of Econometrics, Elsevier, vol. 92(2), pages 325-353, October.
    24. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    25. Alessandro Rossi, 2002. "The Britten-Jones And Neuberger Smile-Consistent With Stochastic Volatility Option Pricing Model: A Further Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-31.
    26. 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.
    27. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    28. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    29. Edoardo Otranto & Giampiero Gallo, 2002. "A Nonparametric Bayesian Approach To Detect The Number Of Regimes In Markov Switching Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 477-496.
    30. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
    31. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    32. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    33. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    34. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    35. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    36. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    2. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    3. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    4. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    5. Laurent Calvet & Adlai Fisher, 2003. "Regime-Switching and the Estimation of Multifractal Processes," NBER Working Papers 9839, National Bureau of Economic Research, Inc.
    6. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, September.
    7. 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.
    8. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    9. 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.
    10. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2015. "Bad environments, good environments: A non-Gaussian asymmetric volatility model," Journal of Econometrics, Elsevier, vol. 186(1), pages 258-275.
    11. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    12. 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).
    13. 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.
    14. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    15. Panos Pouliasis & Ioannis Kyriakou & Nikos Papapostolou, 2017. "On equity risk prediction and tail spillovers," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 22(4), pages 379-393, October.
    16. Richard D. F. Harris & Murat Mazibas, 2022. "A component Markov regime‐switching autoregressive conditional range model," Bulletin of Economic Research, Wiley Blackwell, vol. 74(2), pages 650-683, April.
    17. Issler, João Victor, 1999. "Estimating and forecasting the volatility of Brazilian finance series using arch models (Preliminary Version)," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 347, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    18. 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.
    19. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.

    More about this item

    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

    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:eee:empfin:v:13:y:2006:i:2:p:203-230. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jempfin .

    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.