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

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  • 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.

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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, arXiv.org.
    • Handle: RePEc:arx:papers:0901.1315
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    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. 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.
    3. Bastidon, Cécile & Jawadi, Fredj, 2024. "Trade fragmentation and volatility-of-volatility networks," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 91(C).
    4. 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.
    5. 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.
    6. Yuta Kurose, 2021. "Stochastic volatility model with range-based correction and leverage," Papers 2110.00039, arXiv.org, revised Oct 2021.
    7. 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).
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    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.

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