IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v58y2023ipas154461232300380x.html
   My bibliography  Save this article

Volatility forecast with the regularity modifications

Author

Listed:
  • Zhu, Qinwen
  • Diao, Xundi
  • Wu, Chongfeng

Abstract

The promising empirical results presented using high-frequency data show that the log-volatility behaves essentially as a fractional Brownian motion (fBm) with a Hurst exponent smaller than 0.5. Motivated by these findings, we propose the autoregressive rough volatility (ARRV) model, which combines the fractional Gaussian noise (fGn) process and time series models to forecast volatility. We apply this model to the VIX index by adopting the fBm approximation technique, and our results indicate that the ARRV model can significantly improve VIX out-of-sample forecast accuracy, particularly during turbulent times.

Suggested Citation

  • Zhu, Qinwen & Diao, Xundi & Wu, Chongfeng, 2023. "Volatility forecast with the regularity modifications," Finance Research Letters, Elsevier, vol. 58(PA).
    • Handle: RePEc:eee:finlet:v:58:y:2023:i:pa:s154461232300380x
    DOI: 10.1016/j.frl.2023.104008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S154461232300380X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2023.104008?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. Chen, Cathy W.S. & Hsu, Hsiao-Yun & Watanabe, Toshiaki, 2023. "Tail risk forecasting of realized volatility CAViaR models," Finance Research Letters, Elsevier, vol. 51(C).
    2. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    3. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    4. Boubaker, Sabri & Goodell, John W. & Pandey, Dharen Kumar & Kumari, Vineeta, 2022. "Heterogeneous impacts of wars on global equity markets: Evidence from the invasion of Ukraine," Finance Research Letters, Elsevier, vol. 48(C).
    5. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    6. Hansen, Lars-Peter & Sargent, Thomas-J, 2001. "Acknowledgement Misspecification in Macroeconomic Theory," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 213-227, February.
    7. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    8. Liu, Zhichao & Liu, Jing & Zeng, Qing & Wu, Lan, 2022. "VIX and stock market volatility predictability: A new approach," Finance Research Letters, Elsevier, vol. 48(C).
    9. Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    10. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    11. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    12. Pandey, Dharen Kumar & Kumari, Vineeta, 2021. "Event study on the reaction of the developed and emerging stock markets to the 2019-nCoV outbreak," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 467-483.
    13. Fry-McKibbin, Renée & Greenwood-Nimmo, Matthew & Hsiao, Cody Yu-Ling & Qi, Lin, 2022. "Higher-order comoment contagion among G20 equity markets during the COVID-19 pandemic," Finance Research Letters, Elsevier, vol. 45(C).
    14. Yuan, Ying & Zhang, Tonghui, 2020. "Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    15. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    16. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    17. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2022. "Consistent estimation for fractional stochastic volatility model under high‐frequency asymptotics," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1086-1132, October.
    18. Wang, Jiqian & Lu, Xinjie & He, Feng & Ma, Feng, 2020. "Which popular predictor is more useful to forecast international stock markets during the coronavirus pandemic: VIX vs EPU?," International Review of Financial Analysis, Elsevier, vol. 72(C).
    19. Rahman, Md Lutfur & Amin, Abu & Al Mamun, Mohammed Abdullah, 2021. "The COVID-19 outbreak and stock market reactions: Evidence from Australia," Finance Research Letters, Elsevier, vol. 38(C).
    20. Anthony W. Chen & Jim Chen & V. Reddy Dondeti, 2020. "The US-China trade war: dominance of trade or technology?," Applied Economics Letters, Taylor & Francis Journals, vol. 27(11), pages 904-909, June.
    21. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    22. Abakah, Emmanuel Joel Aikins & Tiwari, Aviral Kumar & Alagidede, Imhotep Paul & Gil-Alana, Luis Alberiko, 2022. "Re-examination of risk-return dynamics in international equity markets and the role of policy uncertainty, geopolitical risk and VIX: Evidence using Markov-switching copulas," Finance Research Letters, Elsevier, vol. 47(PA).
    23. Lars Peter Hansen & Thomas J. Sargent, 2001. "Acknowledging Misspecification in Macroeconomic Theory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July.
    24. Kumari, Vineeta & Kumar, Gaurav & Pandey, Dharen Kumar, 2023. "Are the European Union stock markets vulnerable to the Russia–Ukraine war?," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    25. Omar Euch & Masaaki Fukasawa & Mathieu Rosenbaum, 2018. "The microstructural foundations of leverage effect and rough volatility," Finance and Stochastics, Springer, vol. 22(2), pages 241-280, April.
    Full references (including those not matched with items on IDEAS)

    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. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2024. "Forecasting Daily Volatility of Stock Price Index Using Daily Returns and Realized Volatility," Econometrics and Statistics, Elsevier, vol. 32(C), pages 34-56.
    2. Mathieu Rosenbaum & Jianfei Zhang, 2022. "On the universality of the volatility formation process: when machine learning and rough volatility agree," Papers 2206.14114, arXiv.org.
    3. Alfeus, Mesias & Nikitopoulos, Christina Sklibosios, 2022. "Forecasting volatility in commodity markets with long-memory models," Journal of Commodity Markets, Elsevier, vol. 28(C).
    4. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    5. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2021. "Forecasting Daily Volatility of Stock Price Index Using Daily Returns and Realized Volatility," Discussion paper series HIAS-E-104, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    6. Wang, Ping & Han, Wei & Huang, Chengcheng & Duong, Duy, 2022. "Forecasting realised volatility from search volume and overnight sentiment: Evidence from China," Research in International Business and Finance, Elsevier, vol. 62(C).
    7. Ma, Feng & Wang, Jiqian & Wahab, M.I.M. & Ma, Yuanhui, 2023. "Stock market volatility predictability in a data-rich world: A new insight," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1804-1819.
    8. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    9. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Decoupling the short- and long-term behavior of stochastic volatility," CREATES Research Papers 2017-26, Department of Economics and Business Economics, Aarhus University.
    10. Kelly Trinh & Bo Zhang & Chenghan Hou, 2025. "Macroeconomic real‐time forecasts of univariate models with flexible error structures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(1), pages 59-78, January.
    11. Xu, Yanyan & Huang, Dengshi & Ma, Feng & Qiao, Gaoxiu, 2019. "Liquidity and realized range-based volatility forecasting: Evidence from China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1102-1113.
    12. Sattarhoff, Cristina & Lux, Thomas, 2023. "Forecasting the variability of stock index returns with the multifractal random walk model for realized volatilities," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1678-1697.
    13. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    14. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
    15. Li, Tao & Ma, Feng & Zhang, Xuehua & Zhang, Yaojie, 2020. "Economic policy uncertainty and the Chinese stock market volatility: Novel evidence," Economic Modelling, Elsevier, vol. 87(C), pages 24-33.
    16. Ahmed, Shamima & Assaf, Rima & Rahman, Molla Ramizur & Tabassum, Fariha, 2023. "Is geopolitical risk interconnected? Evidence from Russian-Ukraine crisis," The Journal of Economic Asymmetries, Elsevier, vol. 28(C).
    17. Panagiotidis, Theodore & Papapanagiotou, Georgios & Stengos, Thanasis, 2023. "Dying together: A convergence analysis of fatalities during COVID-19," The Journal of Economic Asymmetries, Elsevier, vol. 28(C).
    18. Paul Gassiat, 2022. "Weak error rates of numerical schemes for rough volatility," Papers 2203.09298, arXiv.org, revised Feb 2023.
    19. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2021. "The Alpha‐Heston stochastic volatility model," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 943-978, July.
    20. Peter K. Friz & Paul Gassiat & Paolo Pigato, 2022. "Short-dated smile under rough volatility: asymptotics and numerics," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 463-480, March.

    More about this item

    Keywords

    Autoregressive rough volatility model; Volatility forecasting; VIX index; High frequency data;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    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:finlet:v:58:y:2023:i:pa:s154461232300380x. 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/frl .

    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.