IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v43y2014icp160-178.html
   My bibliography  Save this article

Discrete stochastic autoregressive volatility

Author

Listed:
  • Cordis, Adriana S.
  • Kirby, Chris

Abstract

We use Markov chain methods to develop a flexible class of discrete stochastic autoregressive volatility (DSARV) models. Our approach to formulating the models is straightforward, and readily accommodates features such as volatility asymmetry and time-varying volatility persistence. Moreover, it produces models with a low-dimensional state space, which greatly enhances computational tractability. We illustrate the proposed methodology for both individual stock and stock index returns, and show that simple first- and second-order DSARV models outperform generalized autoregressive conditional heteroscedasticity and Markov-switching multifractal models in forecasting volatility.

Suggested Citation

  • Cordis, Adriana S. & Kirby, Chris, 2014. "Discrete stochastic autoregressive volatility," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 160-178.
    • Handle: RePEc:eee:jbfina:v:43:y:2014:i:c:p:160-178
    DOI: 10.1016/j.jbankfin.2014.03.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426614001034
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2014.03.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 3-46, National Bureau of Economic Research, Inc.
    3. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    4. Daal, Elton & Naka, Atsuyuki & Yu, Jung-Suk, 2007. "Volatility clustering, leverage effects, and jump dynamics in the US and emerging Asian equity markets," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2751-2769, September.
    5. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    6. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, January.
    7. 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.
    8. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
    9. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    10. 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.
    11. 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.
    12. Hibbert, Ann Marie & Daigler, Robert T. & Dupoyet, Brice, 2008. "A behavioral explanation for the negative asymmetric return-volatility relation," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2254-2266, October.
    13. A. Luceño, 1999. "Discrete approximations to continuous univariate distributions—an alternative to simulation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 345-352, April.
    14. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    15. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    16. 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.
    17. 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.
    18. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    19. 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.
    20. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    21. Park, Beum-Jo, 2011. "Asymmetric herding as a source of asymmetric return volatility," Journal of Banking & Finance, Elsevier, vol. 35(10), pages 2657-2665, October.
    22. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
    23. Fleming, Jeff & Kirby, Chris, 2011. "Long memory in volatility and trading volume," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1714-1726, July.
    24. 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.
    25. Li, Junye, 2011. "Volatility components, leverage effects, and the return-volatility relations," Journal of Banking & Finance, Elsevier, vol. 35(6), pages 1530-1540, June.
    26. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    27. 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.
    28. 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.
    29. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    30. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    31. Jeff Fleming & Chris Kirby, 2013. "Component-Driven Regime-Switching Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 263-301, March.
    32. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    33. repec:bla:jfinan:v:44:y:1989:i:1:p:1-17 is not listed on IDEAS
    34. E. M. R. A. Engel, 1984. "A Unified Approach To The Study Of Sums, Products, Time‐Aggregation And Other Functions Of Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(3), pages 159-171, May.
    35. Andersen, Torben G, 1996. "Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
    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. 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).
    2. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    3. Ying Wang & Hoi Ying Wong, 2017. "VIX Forecast Under Different Volatility Specifications," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(2), pages 131-148, June.
    4. Ying Wang & Sai Tsang Boris Choy & Hoi Ying Wong, 2016. "Bayesian Option Pricing Framework with Stochastic Volatility for FX Data," Risks, MDPI, vol. 4(4), pages 1-12, December.

    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. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    2. 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.
    3. Jeff Fleming & Chris Kirby, 2013. "Component-Driven Regime-Switching Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 263-301, March.
    4. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    5. Sucarrat, Genaro, 2009. "Forecast Evaluation of Explanatory Models of Financial Variability," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-33.
    6. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    7. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    8. Bauwens, Luc & Sucarrat, Genaro, 2010. "General-to-specific modelling of exchange rate volatility: A forecast evaluation," International Journal of Forecasting, Elsevier, vol. 26(4), pages 885-907, October.
    9. Patton, Andrew J. & Sheppard, Kevin, 2009. "Optimal combinations of realised volatility estimators," International Journal of Forecasting, Elsevier, vol. 25(2), pages 218-238.
    10. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    11. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    12. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
    13. Christian T. Brownlees & Giampiero Gallo, 2007. "Volatility Forecasting Using Explanatory Variables and Focused Selection Criteria," Econometrics Working Papers Archive wp2007_04, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    14. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    15. Sharma, Prateek & Vipul,, 2016. "Forecasting stock market volatility using Realized GARCH model: International evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 222-230.
    16. Andrea BUCCI, 2017. "Forecasting Realized Volatility A Review," Journal of Advanced Studies in Finance, ASERS Publishing, vol. 8(2), pages 94-138.
    17. Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
    18. Fabian Hollstein & Marcel Prokopczuk & Chardin Wese Simen, 2020. "The Conditional Capital Asset Pricing Model Revisited: Evidence from High-Frequency Betas," Management Science, INFORMS, vol. 66(6), pages 2474-2494, June.
    19. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    20. 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.

    More about this item

    Keywords

    Markov chain; Time-varying transition probabilities; Discrete autoregressive model; Stochastic volatility; Realized volatility;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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

    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:jbfina:v:43:y:2014:i:c:p:160-178. 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/jbf .

    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.