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


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


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.

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

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    References listed on IDEAS

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    9. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    10. 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.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Papers 0804.0162,
    13. 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.
    14. 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.
    15. repec:dau:papers:123456789/5374 is not listed on IDEAS
    16. L. C. G. Rogers, 1998. "Volatility Estimation with Price Quanta," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 277-290.
    17. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. repec:spr:jqecon:v:15:y:2017:i:2:d:10.1007_s40953-016-0054-3 is not listed on IDEAS
    4. repec:exl:25engi:v:28:y:2017:i:2:p:162-169 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.

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