IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1302.7036.html
   My bibliography  Save this paper

Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility

Author

Listed:
  • Jozef Barunik
  • Jiri Kukacka

Abstract

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Due to the very long sample period we also develop a rolling estimation approach and we find that while in the first half of the period stock markets showed marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets.

Suggested Citation

  • Jozef Barunik & Jiri Kukacka, 2013. "Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility," Papers 1302.7036, arXiv.org, revised May 2013.
  • Handle: RePEc:arx:papers:1302.7036
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1302.7036
    File Function: Latest version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December.
    2. 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.
    3. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    4. Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
    5. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    6. Koh, Seng Kee & Fong, Wai Mun & Chan, Fabrice, 2007. "A Cardan's discriminant approach to predicting currency crashes," Journal of International Money and Finance, Elsevier, vol. 26(1), pages 131-148, February.
    7. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
    8. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Fischer, Edwin O & Jammernegg, Werner, 1986. "Empirical Investigation of a Catastrophe Theory Extension of the Phillips Curve," The Review of Economics and Statistics, MIT Press, vol. 68(1), pages 9-17, February.
    11. Barlevy, Gadi & Veronesi, Pietro, 2003. "Rational panics and stock market crashes," Journal of Economic Theory, Elsevier, vol. 110(2), pages 234-263, June.
    12. Ho, Thomas S Y & Saunders, Anthony, 1980. "A Catastrophe Model of Bank Failure," Journal of Finance, American Finance Association, vol. 35(5), pages 1189-1207, December.
    13. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    14. Levy, Moshe, 2008. "Stock market crashes as social phase transitions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 137-155, January.
    15. Wang, Yaw-Huei & Keswani, Aneel & Taylor, Stephen J., 2006. "The relationships between sentiment, returns and volatility," International Journal of Forecasting, Elsevier, vol. 22(1), pages 109-123.
    16. Lux, Thomas & Marchesi, Michele, 2002. "Journal of economic behavior and organization: special issue on heterogeneous interacting agents in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 143-147, October.
    17. Creedy, John & Lye, Jenny & Martin, Vance L, 1996. "A Non-linear Model of the Real US-UK Exchange Rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 669-686, Nov.-Dec..
    18. Shaffer, Sherrill, 1991. "Structural shifts and the volatility of chaotic markets," Journal of Economic Behavior & Organization, Elsevier, vol. 15(2), pages 201-214, March.
    19. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    20. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-569, May.
    21. Grasman, Raoul & van der Maas, Han L.J. & Wagenmakers, Eric-Jan, 2009. "Fitting the Cusp Catastrophe in R: A cusp Package Primer," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i08).
    22. Finucane, Thomas J., 1991. "Put-Call Parity and Expected Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(4), pages 445-457, December.
    23. Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
    24. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    25. Creedy, John & Martin, Vance, 1993. "Multiple equilibria and hysteresis in simple exchange models," Economic Modelling, Elsevier, vol. 10(4), pages 339-347, October.
    26. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michael S. Harr'e, 2018. "Multi-agent Economics and the Emergence of Critical Markets," Papers 1809.01332, arXiv.org.
    2. Michael S. Harr'e & Adam Harris & Scott McCallum, 2019. "Singularities and Catastrophes in Economics: Historical Perspectives and Future Directions," Papers 1907.05582, arXiv.org.
    3. Kukacka, Jiri & Barunik, Jozef, 2017. "Estimation of financial agent-based models with simulated maximum likelihood," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 21-45.
    4. Wang, J., 2015. "Can a stochastic cusp catastrophe model explain housing market crashes?," CeNDEF Working Papers 15-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    5. Kukacka, Jiri & Kristoufek, Ladislav, 2020. "Do ‘complex’ financial models really lead to complex dynamics? Agent-based models and multifractality," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    6. Mohamed M. Mostafa, 2020. "Catastrophe Theory Predicts International Concern for Global Warming," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 709-731, September.
    7. Dennis Wesselbaum, 2017. "Catastrophe theory and the financial crisis," Scottish Journal of Political Economy, Scottish Economic Society, vol. 64(4), pages 376-391, September.
    8. Bolgorian, Meysam, 2019. "Can a cusp catastrophe model describe the effect of sanctions on exchange rates?," Economics Discussion Papers 2019-2, Kiel Institute for the World Economy (IfW).

    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. Barunik, J. & Vosvrda, M., 2009. "Can a stochastic cusp catastrophe model explain stock market crashes?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1824-1836, October.
    2. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    3. R. P. Brito & H. Sebastião & P. Godinho, 2017. "Portfolio choice with high frequency data: CRRA preferences and the liquidity effect," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 16(2), pages 65-86, August.
    4. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    5. Cherif Guermat & Richard D. F. Harris, 2006. "Bias in the estimation of non-linear transformations of the integrated variance of returns," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(7), pages 481-494.
    6. Warusawitharana, Missaka, 2018. "Time-varying volatility and the power law distribution of stock returns," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 123-141.
    7. Li, Jia & Patton, Andrew J., 2018. "Asymptotic inference about predictive accuracy using high frequency data," Journal of Econometrics, Elsevier, vol. 203(2), pages 223-240.
    8. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, September.
    9. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    10. Denisa Banulescu-Radu & Christophe Hurlin & Bertrand Candelon & Sébastien Laurent, 2016. "Do We Need High Frequency Data to Forecast Variances?," Annals of Economics and Statistics, GENES, issue 123-124, pages 135-174.
    11. Helmut Herwartz, 2006. "Econometric analysis of high frequency data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 89-104, March.
    12. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    13. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2000. "Bifurcation Routes to Volatility Clustering," CeNDEF Working Papers 00-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    14. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    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. repec:zbw:cfswop:wp200508 is not listed on IDEAS
    17. Dinghai Xu, 2019. "A Study on Volatility Spurious Almost Integration Effect: A Threshold Realized GARCH Approach," Working Papers 1903, University of Waterloo, Department of Economics, revised Dec 2019.
    18. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    19. Bekierman, Jeremias & Manner, Hans, 2018. "Forecasting realized variance measures using time-varying coefficient models," International Journal of Forecasting, Elsevier, vol. 34(2), pages 276-287.
    20. António Alberto Santos, 2015. "The evolution of the Volatility in Financial Returns: Realized Volatility vs Stochastic Volatility Measures," GEMF Working Papers 2015-10, GEMF, Faculty of Economics, University of Coimbra.
    21. Michael McAleer & Marcelo C. Medeiros, 2009. "Forecasting Realized Volatility with Linear and Nonlinear Models," CARF F-Series CARF-F-189, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1302.7036. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.