IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v8y2020i2p35-d344228.html
   My bibliography  Save this article

Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

Author

Listed:
  • Moawia Alghalith

    (Department of Economics, University of West Indies, St. Augustine, Trinidad, Trinidad and Tobago)

  • Christos Floros

    (Department of Accounting & Finance, School of Economics & Management Sciences, Hellenic Mediterranean University, Heraklion 71410, Greece)

  • Konstantinos Gkillas

    (Department of Business Administration, University of Patras, Patras 26500, Greece)

Abstract

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasonably accurate. Such evidence implies that the stochastic volatility models proposed in the literature with constant volatility of volatility may fail to approximate the discrete-time short rate dynamics.

Suggested Citation

  • Moawia Alghalith & Christos Floros & Konstantinos Gkillas, 2020. "Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility," Risks, MDPI, vol. 8(2), pages 1-15, April.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:2:p:35-:d:344228
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/8/2/35/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/8/2/35/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    2. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    3. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    4. Massimiliano Caporin & Michael McAleer, 2012. "Do We Really Need Both Bekk And Dcc? A Tale Of Two Multivariate Garch Models," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 736-751, September.
    5. Manabu Asai & Michael McAleer, 2011. "Alternative Asymmetric Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 548-564, October.
    6. Bekaert, Geert & Hoerova, Marie, 2014. "The VIX, the variance premium and stock market volatility," Journal of Econometrics, Elsevier, vol. 183(2), pages 181-192.
    7. 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.
    8. 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.
    9. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    10. Amendola, Alessandra & Storti, Giuseppe, 2009. "Combination of multivariate volatility forecasts," SFB 649 Discussion Papers 2009-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Moawia Alghalith, 2012. "New methods of estimating volatility and returns," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 1-4, February.
    12. Esfandiar Maasoumi & Michael McAleer, 2008. "Realized Volatility and Long Memory: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 1-9.
    13. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    14. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
    15. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    16. 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.
    17. Park, Yang-Ho, 2015. "Volatility-of-volatility and tail risk hedging returns," Journal of Financial Markets, Elsevier, vol. 26(C), pages 38-63.
    18. Mrázek, Milan & Pospíšil, Jan & Sobotka, Tomáš, 2016. "On calibration of stochastic and fractional stochastic volatility models," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1036-1046.
    19. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    20. Moawia Alghalith, 2012. "New methods of estimating volatility and returns: Revisited," Journal of Asset Management, Palgrave Macmillan, vol. 13(5), pages 307-309, October.
    21. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    22. Amendola, Alessandra & Braione, Manuela & Candila, Vincenzo & Storti, Giuseppe, 2020. "A Model Confidence Set approach to the combination of multivariate volatility forecasts," International Journal of Forecasting, Elsevier, vol. 36(3), pages 873-891.
    23. 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..
    24. Reno, Roberto, 2006. "Nonparametric estimation of stochastic volatility models," Economics Letters, Elsevier, vol. 90(3), pages 390-395, March.
    25. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    26. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    27. F. Comte & V. Genon-Catalot & Y. Rozenholc, 2010. "Nonparametric estimation for a stochastic volatility model," Finance and Stochastics, Springer, vol. 14(1), pages 49-80, January.
    28. Moawia Alghalith, 2016. "Estimating the Stock/Portfolio Volatility and the Volatility of Volatility: A New Simple Method," Econometric Reviews, Taylor & Francis Journals, vol. 35(2), pages 257-262, February.
    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. Christos Floros & Konstantinos Gkillas & Christoforos Konstantatos & Athanasios Tsagkanos, 2020. "Realized Measures to Explain Volatility Changes over Time," JRFM, MDPI, vol. 13(6), pages 1-19, June.
    2. Loretta Mastroeni, 2022. "Pricing Options with Vanishing Stochastic Volatility," Risks, MDPI, vol. 10(9), pages 1-16, September.
    3. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.

    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. Athanasios Tsagkanos & Konstantinos Gkillas & Christoforos Konstantatos & Christos Floros, 2021. "Does Trading Volume Drive Systemic Banks’ Stock Return Volatility? Lessons from the Greek Banking System," IJFS, MDPI, vol. 9(2), pages 1-13, April.
    2. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    3. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    4. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    5. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, August.
    6. Toshiaki Ogawa & Masato Ubukata & Toshiaki Watanabe, 2020. "Stock Return Predictability and Variance Risk Premia around the ZLB," IMES Discussion Paper Series 20-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    7. Christos Floros & Konstantinos Gkillas & Christoforos Konstantatos & Athanasios Tsagkanos, 2020. "Realized Measures to Explain Volatility Changes over Time," JRFM, MDPI, vol. 13(6), pages 1-19, June.
    8. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    9. Enrique Ter Horst & Abel Rodriguez & Henryk Gzyl & German Molina, 2012. "Stochastic volatility models including open, close, high and low prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 199-212, May.
    10. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2017. "Realized stochastic volatility with general asymmetry and long memory," Journal of Econometrics, Elsevier, vol. 199(2), pages 202-212.
    11. Manabu Asai & Michael McAleer, 2017. "A fractionally integrated Wishart stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 42-59, March.
    12. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.
    13. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2012. "Asymmetry and Long Memory in Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 495-512, June.
    14. Asai, Manabu & Caporin, Massimiliano & McAleer, Michael, 2015. "Forecasting Value-at-Risk using block structure multivariate stochastic volatility models," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 40-50.
    15. Yang Shen, 2020. "Effect of Variance Swap in Hedging Volatility Risk," Risks, MDPI, vol. 8(3), pages 1-34, July.
    16. Chen, Cathy W.S. & Watanabe, Toshiaki & Lin, Edward M.H., 2023. "Bayesian estimation of realized GARCH-type models with application to financial tail risk management," Econometrics and Statistics, Elsevier, vol. 28(C), pages 30-46.
    17. Liu, Chang & Chang, Chuo, 2021. "Combination of transition probability distribution and stable Lorentz distribution in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    18. Casas, Isabel & Gao, Jiti, 2008. "Econometric estimation in long-range dependent volatility models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 72-83, November.
    19. Ma, Feng & Wahab, M.I.M. & Zhang, Yaojie, 2019. "Forecasting the U.S. stock volatility: An aligned jump index from G7 stock markets," Pacific-Basin Finance Journal, Elsevier, vol. 54(C), pages 132-146.

    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:gam:jrisks:v:8:y:2020:i:2:p:35-:d:344228. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.