IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i15p1794-d603655.html
   My bibliography  Save this article

Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility

Author

Listed:
  • Eduardo Ramos-Pérez

    (Faculty of Economics, Universidad de Alcalá, Plaza de la Victoria 2, 28802 Alcalá de Henares, Madrid, Spain)

  • Pablo J. Alonso-González

    (Economics Department, Universidad de Alcalá, Plaza de la Victoria 2, 28802 Alcalá de Henares, Madrid, Spain)

  • José Javier Núñez-Velázquez

    (Economics Department, Universidad de Alcalá, Plaza de la Victoria 2, 28802 Alcalá de Henares, Madrid, Spain)

Abstract

Events such as the Financial Crisis of 2007–2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management function able to implement effective hedging strategies. Stock volatility forecasts play a key role in the estimation of equity risk and, thus, in the management actions carried out by financial institutions. Therefore, this paper has the aim of proposing more accurate stock volatility models based on novel machine and deep learning techniques. This paper introduces a neural network-based architecture, called Multi-Transformer. Multi-Transformer is a variant of Transformer models, which have already been successfully applied in the field of natural language processing. Indeed, this paper also adapts traditional Transformer layers in order to be used in volatility forecasting models. The empirical results obtained in this paper suggest that the hybrid models based on Multi-Transformer and Transformer layers are more accurate and, hence, they lead to more appropriate risk measures than other autoregressive algorithms or hybrid models based on feed forward layers or long short term memory cells.

Suggested Citation

  • Eduardo Ramos-Pérez & Pablo J. Alonso-González & José Javier Núñez-Velázquez, 2021. "Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility," Mathematics, MDPI, vol. 9(15), pages 1-18, July.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1794-:d:603655
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/15/1794/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/15/1794/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    3. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    6. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    7. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    8. Amit Goyal & Ivo Welch, 2003. "Predicting the Equity Premium with Dividend Ratios," Management Science, INFORMS, vol. 49(5), pages 639-654, May.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. 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.
    11. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    12. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    13. Amit Goyal & Ivo Welch, 2003. "Predicting the Equity Premium with Dividend Ratios," Management Science, INFORMS, vol. 49(5), pages 639-654, May.
    14. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836.
    15. Gunho Jung & Sun-Yong Choi & Benjamin Miranda Tabak, 2021. "Forecasting Foreign Exchange Volatility Using Deep Learning Autoencoder-LSTM Techniques," Complexity, Hindawi, vol. 2021, pages 1-16, March.
    16. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    17. Tanya Molodtsova & David H. Papell, 2013. "Taylor Rule Exchange Rate Forecasting during the Financial Crisis," NBER International Seminar on Macroeconomics, University of Chicago Press, vol. 9(1), pages 55-97.
    18. 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.
    19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    20. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    21. 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.
    22. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    23. Swanson, Norman R., 1998. "Money and output viewed through a rolling window," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 455-474, May.
    24. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    25. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 211-250.
    26. Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, vol. 8(2), pages 151-165, November.
    27. 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..
    28. Sauraj Verma, 2021. "Forecasting volatility of crude oil futures using a GARCH–RNN hybrid approach," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 28(2), pages 130-142, April.
    29. 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.
    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. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2021. "Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility," Papers 2109.12621, arXiv.org.
    2. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    3. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    5. 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.
    6. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    7. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    8. 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.
    9. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    10. Wang, Yudong & Wu, Chongfeng, 2012. "Forecasting energy market volatility using GARCH models: Can multivariate models beat univariate models?," Energy Economics, Elsevier, vol. 34(6), pages 2167-2181.
    11. 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.
    12. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    13. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    14. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47.
    15. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    16. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    17. Cristina Amado & Annastiina Silvennoinen & Timo Teräsvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," CREATES Research Papers 2018-14, Department of Economics and Business Economics, Aarhus University.
    18. DAVID G. McMILLAN & ALAN E. H. SPEIGHT, 2007. "Value‐at‐Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric, and Long‐Memory GARCH Models," International Review of Finance, International Review of Finance Ltd., vol. 7(1‐2), pages 1-19, March.
    19. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    20. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.

    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:jmathe:v:9:y:2021:i:15:p:1794-:d:603655. 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.