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SpotV2Net: Multivariate intraday spot volatility forecasting via vol-of-vol-informed graph attention networks

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  • Brini, Alessio
  • Toscano, Giacomo

Abstract

This paper introduces SpotV2Net, a multivariate intraday spot volatility forecasting model based on a graph attention network architecture. SpotV2Net represents assets as nodes within a graph and includes non-parametric high-frequency Fourier estimates of the spot volatility and co-volatility as node features. Further, it incorporates Fourier estimates of the spot volatility of volatility and co-volatility of volatility as features for node edges, to capture spillover effects. We test the forecasting accuracy of SpotV2Net in an extensive empirical exercise, conducted with the components of the Dow Jones Industrial Average index. The results we obtain suggest that SpotV2Net yields statistically significant gains in forecasting accuracy, for both single-step and multi-step forecasts, compared to a panel heterogeneous autoregressive model and alternative machine-learning models. To interpret the forecasts produced by SpotV2Net, we employ GNNExplainer (Ying et al., 2019), a model-agnostic interpretability tool, and thereby uncover subgraphs that are critical to a node’s predictions.

Suggested Citation

  • Brini, Alessio & Toscano, Giacomo, 2025. "SpotV2Net: Multivariate intraday spot volatility forecasting via vol-of-vol-informed graph attention networks," International Journal of Forecasting, Elsevier, vol. 41(3), pages 1093-1111.
  • Handle: RePEc:eee:intfor:v:41:y:2025:i:3:p:1093-1111
    DOI: 10.1016/j.ijforecast.2024.11.004
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    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Maria Elvira Mancino & Tommaso Mariotti & Giacomo Toscano, 2022. "Asymptotic Normality for the Fourier spot volatility estimator in the presence of microstructure noise," Papers 2209.08967, arXiv.org.
    3. Ding, Yashuang (Dexter), 2023. "A simple joint model for returns, volatility and volatility of volatility," Journal of Econometrics, Elsevier, vol. 232(2), pages 521-543.
    4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    5. 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.
    6. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    7. Andrea Bucci, 2020. "Realized Volatility Forecasting with Neural Networks," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 502-531.
    8. Eduardo Rossi & Dean Fantazzini, 2015. "Long Memory and Periodicity in Intraday Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 13(4), pages 922-961.
    9. Chao Zhang & Yihuang Zhang & Mihai Cucuringu & Zhongmin Qian, 2022. "Volatility forecasting with machine learning and intraday commonality," Papers 2202.08962, arXiv.org, revised Feb 2023.
    10. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    11. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    12. Tim Bollerslev & Nour Meddahi & Serge Luther Nyawa Womo, 2019. "High-dimensional multivariate realized volatility estimation," Post-Print hal-04947294, HAL.
    13. Huang, Darien & Schlag, Christian & Shaliastovich, Ivan & Thimme, Julian, 2019. "Volatility-of-Volatility Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 54(6), pages 2423-2452, December.
    14. Sanfelici, Simona & Toscano, Giacomo, 2024. "The Fourier–Malliavin Volatility (FMVol) MATLAB® library," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 338-353.
    15. Rafael Reisenhofer & Xandro Bayer & Nikolaus Hautsch, 2022. "HARNet: A Convolutional Neural Network for Realized Volatility Forecasting," Papers 2205.07719, arXiv.org.
    16. 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.
    17. Qiong Wu & Christopher G. Brinton & Zheng Zhang & Andrea Pizzoferrato & Zhenming Liu & Mihai Cucuringu, 2019. "Equity2Vec: End-to-end Deep Learning Framework for Cross-sectional Asset Pricing," Papers 1909.04497, arXiv.org, revised Oct 2021.
    18. Behrendt, Simon & Schmidt, Alexander, 2018. "The Twitter myth revisited: Intraday investor sentiment, Twitter activity and individual-level stock return volatility," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 355-367.
    19. Herskovic, Bernard & Kelly, Bryan & Lustig, Hanno & Van Nieuwerburgh, Stijn, 2016. "The common factor in idiosyncratic volatility: Quantitative asset pricing implications," Journal of Financial Economics, Elsevier, vol. 119(2), pages 249-283.
    20. Kim Christensen & Mathias Siggaard & Bezirgen Veliyev, 2023. "A Machine Learning Approach to Volatility Forecasting," Journal of Financial Econometrics, Oxford University Press, vol. 21(5), pages 1680-1727.
    21. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    22. Ligot, Stephanie & Gillet, Roland & Veryzhenko, Iryna, 2021. "Intraday volatility smile: Effects of fragmentation and high frequency trading on price efficiency," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    23. Lin, Weidong & Taamouti, Abderrahim, 2024. "Portfolio selection under non-gaussianity and systemic risk: A machine learning based forecasting approach," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1179-1188.
    24. Fei Liu & Athanasios A. Pantelous & Hans-Jörg von Mettenheim, 2018. "Forecasting and trading high frequency volatility on large indices," Quantitative Finance, Taylor & Francis Journals, vol. 18(5), pages 737-748, May.
    25. 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.
    26. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2223-2273.
    27. Brailsford, Timothy J. & Faff, Robert W., 1996. "An evaluation of volatility forecasting techniques," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 419-438, April.
    28. Yu Zhao & Shaopeng Wei & Yu Guo & Qing Yang & Xingyan Chen & Qing Li & Fuzhen Zhuang & Ji Liu & Gang Kou, 2022. "Combining Intra-Risk and Contagion Risk for Enterprise Bankruptcy Prediction Using Graph Neural Networks," Papers 2202.03874, arXiv.org, revised Jul 2022.
    29. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    30. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
    31. Fei Sun & Yijun Hu, 2018. "Quasiconvex risk measures with markets volatility," Papers 1806.08701, arXiv.org, revised Jun 2019.
    32. Chao Zhang & Xingyue Pu & Mihai Cucuringu & Xiaowen Dong, 2023. "Graph Neural Networks for Forecasting Multivariate Realized Volatility with Spillover Effects," Papers 2308.01419, arXiv.org.
    33. Stephanie Ligot & Roland Gillet & Iryna Veryzhenko, 2021. "Intraday volatility smile: Effects of fragmentation and high frequency trading on price efficiency," Post-Print hal-03905487, HAL.
    34. João F. Caldeira & Guilherme V. Moura & Francisco J. Nogales & André A. P. Santos, 2017. "Combining Multivariate Volatility Forecasts: An Economic-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 15(2), pages 247-285.
    35. Bollerslev, Tim & Meddahi, Nour & Nyawa, Serge, 2019. "High-dimensional multivariate realized volatility estimation," Journal of Econometrics, Elsevier, vol. 212(1), pages 116-136.
    36. James B. Heaton & Nicholas Polson & Jan H. Witte, 2017. "Rejoinder to ‘Deep learning for finance: deep portfolios’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(1), pages 19-21, January.
    37. Fei Sun & Yijun Hu, 2018. "Systemic risk measures with markets volatility," Papers 1812.06185, arXiv.org, revised Jun 2019.
    38. Bernard Herskovic & Bryan Kelly & Hanno Lustig & Stijn Van Nieuwerburgh, 2020. "Firm Volatility in Granular Networks," Journal of Political Economy, University of Chicago Press, vol. 128(11), pages 4097-4162.
    39. Michael Donadelli & Marcus Jüppner & Antonio Paradiso & Christian Schlag, 2019. "Temperature Volatility Risk," Working Papers 2019:05, Department of Economics, University of Venice "Ca' Foscari".
    40. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
    41. Simona Sanfelici & Giacomo Toscano, 2024. "The Fourier-Malliavin Volatility (FMVol) MATLAB library," Papers 2402.00172, arXiv.org.
    42. Michael Goldstein & Amy Kwan & Richard Philip, 2023. "High-Frequency Trading Strategies," Management Science, INFORMS, vol. 69(8), pages 4413-4434, August.
    43. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," Review of Finance, European Finance Association, vol. 33(5), pages 2223-2273.
    44. Li, Leon, 2022. "The dynamic interrelations of oil-equity implied volatility indexes under low and high volatility-of-volatility risk," Energy Economics, Elsevier, vol. 105(C).
    45. Nishimura, Yusaku & Sun, Bianxia, 2018. "The intraday volatility spillover index approach and an application in the Brexit vote," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 55(C), pages 241-253.
    46. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    47. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    48. Zhu, Haibin & Bai, Lu & He, Lidan & Liu, Zhi, 2023. "Forecasting realized volatility with machine learning: Panel data perspective," Journal of Empirical Finance, Elsevier, vol. 73(C), pages 251-271.
    49. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    50. Giacomo Toscano & Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2021. "Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts," Papers 2112.14529, arXiv.org, revised Sep 2022.
    51. Laurent A. F. Callot & Anders B. Kock & Marcelo C. Medeiros, 2017. "Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 140-158, January.
    52. Emilio Barucci & Maria Elvira Mancino, 2010. "Computation Of Volatility In Stochastic Volatility Models With High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 767-787.
    53. Junjie Hu & Wolfgang Karl Hardle & Weiyu Kuo, 2019. "Risk of Bitcoin Market: Volatility, Jumps, and Forecasts," Papers 1912.05228, arXiv.org, revised Dec 2021.
    54. Allaj, Erindi & Sanfelici, Simona, 2023. "Early Warning Systems for identifying financial instability," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1777-1803.
    55. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2015. "Intra-daily volatility spillovers in international stock markets," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 95-114.
    56. Wilms, Ines & Rombouts, Jeroen & Croux, Christophe, 2021. "Multivariate volatility forecasts for stock market indices," International Journal of Forecasting, Elsevier, vol. 37(2), pages 484-499.
    57. Xue, Yi & Gençay, Ramazan, 2012. "Trading frequency and volatility clustering," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 760-773.
    58. Tommaso Mariotti & Fabrizio Lillo & Giacomo Toscano, 2023. "From zero-intelligence to queue-reactive: limit-order-book modeling for high-frequency volatility estimation and optimal execution," Quantitative Finance, Taylor & Francis Journals, vol. 23(3), pages 367-388, March.
    59. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    60. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "High frequency volatility co-movements in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 62(C), pages 35-52.
    61. Becker, R. & Clements, A.E. & Doolan, M.B. & Hurn, A.S., 2015. "Selecting volatility forecasting models for portfolio allocation purposes," International Journal of Forecasting, Elsevier, vol. 31(3), pages 849-861.
    62. 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.
    63. Fredj Jawadi & Waël Louhichi & Abdoulkarim Idi Cheffou, 2015. "Intraday bidirectional volatility spillover across international stock markets: does the global financial crisis matter?," Applied Economics, Taylor & Francis Journals, vol. 47(34-35), pages 3633-3650, July.
    64. Fassas, Athanasios P. & Siriopoulos, Costas, 2019. "Intraday price discovery and volatility spillovers in an emerging market," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 333-346.
    65. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 317-340, December.
    66. Bandi, Federico M. & Russell, Jeffrey R. & Yang, Chen, 2008. "Realized volatility forecasting and option pricing," Journal of Econometrics, Elsevier, vol. 147(1), pages 34-46, November.
    67. Maria Elvira Mancino & Maria Cristina Recchioni, 2015. "Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-33, September.
    68. Raehyun Kim & Chan Ho So & Minbyul Jeong & Sanghoon Lee & Jinkyu Kim & Jaewoo Kang, 2019. "HATS: A Hierarchical Graph Attention Network for Stock Movement Prediction," Papers 1908.07999, arXiv.org, revised Nov 2019.
    69. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    70. Naeem, Muhammad Abubakr & Karim, Sitara & Yarovaya, Larisa & Lucey, Brian M., 2023. "COVID-induced sentiment and the intraday volatility spillovers between energy and other ETFs," Energy Economics, Elsevier, vol. 122(C).
    71. J. B. Heaton & N. G. Polson & J. H. Witte, 2017. "Deep learning for finance: deep portfolios," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(1), pages 3-12, January.
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