IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0901.1315.html
   My bibliography  Save this paper

Stochastic Volatility Models Including Open, Close, High and Low Prices

Author

Listed:
  • Abel Rodriguez
  • Henryk Gzyl
  • German Molina
  • Enrique ter Horst

Abstract

Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility models that uses opening and closing prices along with the minimum and maximum prices within a trading period to infer the dynamics underlying the volatility process of asset prices and compares it with similar models that have been previously presented in the literature. The paper also discusses sequential Monte Carlo algorithms to fit this class of models and illustrates its features using both a simulation study and data form the SP500 index.

Suggested Citation

  • Abel Rodriguez & Henryk Gzyl & German Molina & Enrique ter Horst, 2009. "Stochastic Volatility Models Including Open, Close, High and Low Prices," Papers 0901.1315, arXiv.org.
    • Handle: RePEc:arx:papers:0901.1315
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0901.1315
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    3. L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Papers 0804.0162, arXiv.org.
    4. Jean‐Michel Courtault & Yuri Kabanov & Bernard Bru & Pierre Crépel & Isabelle Lebon & Arnaud Le Marchand, 2000. "Louis Bachelier on the Centenary of Théorie de la Spéculation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 339-353, July.
    5. L. C. G. Rogers, 1998. "Volatility Estimation with Price Quanta," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 277-290, July.
    6. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    7. 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.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    10. Jeffrey R. Russell & Robert F. Engle, 1998. "Econometric Analysis of Discrete-valued Irregularly-spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model," CRSP working papers 470, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    11. Malik Magdon-Ismail & Amir Atiya, 2003. "A maximum likelihood approach to volatility estimation for a Brownian motion using high, low and close price data," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 376-384.
    12. 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.
    13. 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.
    14. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
    15. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    16. 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.
    17. Ball, Clifford A & Torous, Walter N, 1984. "The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing," The Journal of Business, University of Chicago Press, vol. 57(1), pages 97-112, January.
    18. Officer, R R, 1973. "The Variability of the Market Factor of the New York Stock Exchange," The Journal of Business, University of Chicago Press, vol. 46(3), pages 434-453, July.
    19. G. Huerta & M. West, 1999. "Priors and component structures in autoregressive time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 881-899.
    20. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    21. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    22. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    23. repec:dau:papers:123456789/5374 is not listed on IDEAS
    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. Parthajit Kayal & S. Maheswaran, 2017. "Is USD-INR Really an Excessively Volatile Currency Pair?," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 15(2), pages 329-342, June.
    2. Bastidon, Cécile & Jawadi, Fredj, 2024. "Trade fragmentation and volatility-of-volatility networks," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 91(C).
    3. Muneer Shaik & S. Maheswaran, 2019. "Robust Volatility Estimation with and Without the Drift Parameter," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 57-91, March.
    4. Yuta Kurose, 2021. "Stochastic volatility model with range-based correction and leverage," Papers 2110.00039, arXiv.org, revised Oct 2021.
    5. Ahmed, Walid M.A., 2020. "Is there a risk-return trade-off in cryptocurrency markets? The case of Bitcoin," Journal of Economics and Business, Elsevier, vol. 108(C).
    6. Suk Joon Byun & Jung‐Soon Hyun & Woon Jun Sung, 2021. "Estimation of stochastic volatility and option prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(3), pages 349-360, March.
    7. Nijolė MAKNICKIENĖ & Jelena STANKEVIČIENĖ & Algirdas MAKNICKAS, 2020. "Comparison of Forex Market Forecasting Tools Based on Evolino Ensemble and Technical Analysis Indicators," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 134-148, September.
    8. Dilip Kumar, 2020. "Value-at-Risk in the Presence of Structural Breaks Using Unbiased Extreme Value Volatility Estimator," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 587-610, September.
    9. Kumar, Dilip & Maheswaran, S., 2014. "A reflection principle for a random walk with implications for volatility estimation using extreme values of asset prices," Economic Modelling, Elsevier, vol. 38(C), pages 33-44.
    10. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    11. Parthajit Kayal & Sumanjay Dutta & Vipul Khandelwal & Rakesh Nigam, 2021. "Information Theoretic Ranking of Extreme Value Returns," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 1-21, March.
    12. Ahmed, Walid M.A., 2021. "Stock market reactions to upside and downside volatility of Bitcoin: A quantile analysis," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    13. Kumar, Dilip & Maheswaran, S., 2014. "Modeling and forecasting the additive bias corrected extreme value volatility estimator," International Review of Financial Analysis, Elsevier, vol. 34(C), pages 166-176.
    14. Dilip Kumar, 2016. "Estimating and forecasting value-at-risk using the unbiased extreme value volatility estimator," Proceedings of Economics and Finance Conferences 3205528, International Institute of Social and Economic Sciences.
    15. Dilip Kumar, 2018. "Modeling and Forecasting Unbiased Extreme Value Volatility Estimator in Presence of Leverage Effect," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(2), pages 313-335, June.
    16. Kazemilari, Mansooreh & Djauhari, Maman Abdurachman, 2015. "Correlation network analysis for multi-dimensional data in stocks market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 62-75.
    17. Maheswaran, S. & Kumar, Dilip, 2013. "An automatic bias correction procedure for volatility estimation using extreme values of asset prices," Economic Modelling, Elsevier, vol. 33(C), pages 701-712.
    18. Parthajit Kayal & Sumanjay Dutta & Vipul Khandelwal, "undated". "Information Theoretic Ranking of Extreme Value Returns," Working Papers 2020-195, Madras School of Economics,Chennai,India.

    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. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    4. Lakshmi Padmakumari & S Maheswaran, 2016. "A Regression Based Approach to Capturing the Level Dependence in the Volatility of Stock Returns," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 6(12), pages 706-718, December.
    5. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    6. Muneer Shaik & S. Maheswaran, 2019. "Robust Volatility Estimation with and Without the Drift Parameter," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 57-91, March.
    7. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.
    8. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    9. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. 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.
    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. Dimitrios P. Louzis & Spyros Xanthopoulos‐Sisinis & Apostolos P. Refenes, 2013. "The Role of High‐Frequency Intra‐daily Data, Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 561-576, September.
    14. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2001. "High- and Low-Frequency Exchange Rate Volatility Dynamics: Range-Based Estimation of Stochastic Volatility Models," NBER Working Papers 8162, National Bureau of Economic Research, Inc.
    15. Lyócsa, Štefan & Molnár, Peter & Výrost, Tomáš, 2021. "Stock market volatility forecasting: Do we need high-frequency data?," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1092-1110.
    16. Torben G. Andersen & Tim Bollerslev, 1997. "Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts," NBER Working Papers 6023, National Bureau of Economic Research, Inc.
    17. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    18. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    19. Christensen, Kim & Podolski, Mark, 2005. "Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale," Technical Reports 2005,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.

    More about this item

    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:arx:papers:0901.1315. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.