IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v27y2020i3d10.1007_s10690-019-09299-9.html
   My bibliography  Save this article

Volatility Flocking by Cucker–Smale Mechanism in Financial Markets

Author

Listed:
  • Hyeong-Ohk Bae

    (Ajou University)

  • Seung-Yeal Ha

    (Seoul National University)

  • Yongsik Kim

    (Korea Asset Pricing)

  • Hyuncheul Lim

    (Chonnam National University)

  • Jane Yoo

    (Ajou University)

Abstract

We analyze empirical evidence of flocking stock volatilities according to the Cucker–Smale (C–S) mechanism. By using daily realized volatilities of stocks listed on Dow Jones Industrial Average from January, 2007 to December, 2009, we calibrate key parameters such as time-varying coupling strength, communication weight and stochastic noise in coupling of a benchmark C–S model in Bae et al. (Math Models Methods Appl Sci 25:1299–1335, 2015). Our numerical solutions show that the flocking mechanism explains average volatility dynamics better than a stochastic volatility model without the mechanism over the sample period. The model’s empirical implications are found from cyclicality of Volatility Flocking Index (VFI), an aggregate measure of differences between volatilities. Results from Granger causality tests after vector autoregression estimation show that VFI helps us predict the implied volatility index, and weighted average return of S&P500 Index.

Suggested Citation

  • Hyeong-Ohk Bae & Seung-Yeal Ha & Yongsik Kim & Hyuncheul Lim & Jane Yoo, 2020. "Volatility Flocking by Cucker–Smale Mechanism in Financial Markets," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(3), pages 387-414, September.
    • Handle: RePEc:kap:apfinm:v:27:y:2020:i:3:d:10.1007_s10690-019-09299-9
    DOI: 10.1007/s10690-019-09299-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10690-019-09299-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10690-019-09299-9?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. 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.
    2. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    3. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083, January.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. C. M. Hafner & H. Herwartz, 1998. "Structural analysis of portfolio risk using beta impulse response functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(3), pages 336-355, November.
    7. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    8. 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.
    9. 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.
    10. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," Center for Financial Institutions Working Papers 02-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
    12. Herwartz, H., 1998. "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," SFB 373 Discussion Papers 1998,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    14. Avery, Christopher & Zemsky, Peter, 1998. "Multidimensional Uncertainty and Herd Behavior in Financial Markets," American Economic Review, American Economic Association, vol. 88(4), pages 724-748, September.
    15. Galam, Serge & Zucker, Jean-Daniel, 2000. "From individual choice to group decision-making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 644-659.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    17. Andreas Park & Hamid Sabourian, 2011. "Herding and Contrarian Behavior in Financial Markets," Econometrica, Econometric Society, vol. 79(4), pages 973-1026, July.
    18. John R. Graham, 1999. "Herding among Investment Newsletters: Theory and Evidence," Journal of Finance, American Finance Association, vol. 54(1), pages 237-268, February.
    19. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    20. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    21. Wagner, Friedrich, 2003. "Volatility cluster and herding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 607-619.
    22. 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.
    23. Natividad Blasco & Pilar Corredor & Sandra Ferreruela, 2012. "Does herding affect volatility? Implications for the Spanish stock market," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 311-327, July.
    24. C.K. Chandrasekhar & H. Bagyalakshmi & M.R. Srinivasan & M. Gallo, 2016. "Partial ridge regression under multicollinearity," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2462-2473, October.
    25. Lin, Wen-Ling & Engle, Robert F & Ito, Takatoshi, 1994. "Do Bulls and Bears Move across Borders? International Transmission of Stock Returns and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 7(3), pages 507-538.
    26. Hamao, Yasushi & Masulis, Ronald W & Ng, Victor, 1990. "Correlations in Price Changes and Volatility across International Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 281-307.
    27. Andersen, Torben G, 1996. "Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
    28. 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.
    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. 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.
    2. 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.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Patricia Chelley-Steeley & James Steeley, 2005. "The leverage effect in the UK stock market," Applied Financial Economics, Taylor & Francis Journals, vol. 15(6), pages 409-423.
    5. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    7. 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.
    8. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    9. Robert F. Engle & Emil N. Siriwardane, 2018. "Structural GARCH: The Volatility-Leverage Connection," Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 449-492.
    10. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47.
    11. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    12. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    13. Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2008. "Dynamic Stock Market Interactions between the Canadian, Mexican, and the United States Markets: The NAFTA Experience," Working papers 2008-49, University of Connecticut, Department of Economics.
    14. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
    15. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    16. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    17. Le Pen, Yannick & Sévi, Benoît, 2010. "Volatility transmission and volatility impulse response functions in European electricity forward markets," Energy Economics, Elsevier, vol. 32(4), pages 758-770, July.
    18. 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.
    19. Taylor, James W., 2004. "Volatility forecasting with smooth transition exponential smoothing," International Journal of Forecasting, Elsevier, vol. 20(2), pages 273-286.
    20. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.

    More about this item

    Keywords

    Cucker–Smale model; Communication weight; Flocking; Ridge regression; Volatility-Flocking Index (VFI);
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:kap:apfinm:v:27:y:2020:i:3:d:10.1007_s10690-019-09299-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.