IDEAS home Printed from https://ideas.repec.org/p/ams/ndfwpp/00-04.html
   My bibliography  Save this paper

Bifurcation Routes to Volatility Clustering

Author

Listed:
  • Gaunersdorfer, A.

    () (University of Vienna)

  • Hommes, C.H.

    () (Universiteit van Amsterdam)

  • Wagener, F.O.O.

    () (Universiteit van Amsterdam)

Abstract

See also the publication 'Bifurcation Routes to Volatility Clustering under Evolutionary Learning' in the 'Journal of Economic Behavior & Organization'. Volume 67(1), pp. 27-47. A simple asset pricing model with two types of adaptively learning traders,fundamentalists and technical analysts, is studied. Fractions of these tradertypes, which are both boundedly rational, change over time according toevolutionary learning, with technical analysts conditioning their forecastingrule upon deviations from a benchmark fundamental. Volatility clustering arisesendogenously in this model. Two mechanisms are proposed as an explanation. Thefirst is coexistence of a stable steady state and a stable limit cycle, whicharise as a consequence of a so-called Chenciner bifurcation of the system. Thesecond is intermittency and associated bifurcation routes to strange attractors.Both phenomena are persistent and occur generically in nonlinearmulti-agent evolutionary systems.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
    • Handle: RePEc:ams:ndfwpp:00-04
    as

    Download full text from publisher

    File URL: http://www1.feb.uva.nl/download/GauHomWagSept2000.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. Pintus, Patrick & Sands, Duncan & de Vilder, Robin, 2000. "On the transition from local regular to global irregular fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 247-272, February.
    3. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    4. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    5. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
    6. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    7. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    8. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    9. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
    10. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
    11. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    12. Farmer, J. Doyne & Joshi, Shareen, 2002. "The price dynamics of common trading strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 149-171, October.
    13. C. H. Hommes, 2001. "Financial markets as nonlinear adaptive evolutionary systems," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 149-167.
    14. 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..
    15. Schonhofer, Martin, 1999. "Chaotic Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 89(1), pages 1-20, November.
    16. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    17. William A. Brock, 1993. "Pathways to randomness in the economy: Emergent nonlinearity and chaos in economics and finance," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 3-55.
    18. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    19. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    20. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    21. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    22. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    23. Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June.
    24. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
    25. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695.
    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. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment," Research Paper Series 142, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Brock,W.A. & Hommes,C.H., 2001. "Evolutionary dynamics in financial markets with many trader types," Working papers 7, Wisconsin Madison - Social Systems.
    3. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    4. Dieci, Roberto & Foroni, Ilaria & Gardini, Laura & He, Xue-Zhong, 2006. "Market mood, adaptive beliefs and asset price dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 520-534.
    5. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    6. Ilaria Foroni & Anna Agliari, 2008. "Complex Price Dynamics in a Financial Market with Imitation," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 21-36, September.
    7. Mikhail Anufriev & Cars Hommes, 2012. "Evolutionary Selection of Individual Expectations and Aggregate Outcomes in Asset Pricing Experiments," American Economic Journal: Microeconomics, American Economic Association, vol. 4(4), pages 35-64, November.
    8. Hommes, C.H., 2001. "Modeling the stylized facts in finance through simple nonlinear adaptive systems," CeNDEF Working Papers 01-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. Michael Neugart & Jan Tuinstra, 2003. "Endogenous fluctuations in the demand for education," Journal of Evolutionary Economics, Springer, vol. 13(1), pages 29-51, February.
    10. Chiarella, Carl & He, Xue-Zhong & Wang, Duo, 2006. "A behavioral asset pricing model with a time-varying second moment," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 535-555.
    11. S. Borovkova & H. Dehling & J. Renkema & H. Tulleken, 2003. "A Potential-Field Approach to Financial Time Series Modelling," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 139-161, October.
    12. Andrea Morone, 2008. "Financial markets in the laboratory: an experimental analysis of some stylized facts," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 513-532.
    13. Amilon, Henrik, 2008. "Estimation of an adaptive stock market model with heterogeneous agents," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 342-362, March.
    14. Alfarano, Simone & Lux, Thomas, 2007. "A Noise Trader Model As A Generator Of Apparent Financial Power Laws And Long Memory," Macroeconomic Dynamics, Cambridge University Press, vol. 11(S1), pages 80-101, November.
    15. Alfarano, Simone & Lux, Thomas, 2003. "A minimal noise trader model with realistic time series properties," Economics Working Papers 2003-15, Christian-Albrechts-University of Kiel, Department of Economics.
    16. Verbic, Miroslav, 2006. "Memory and Asset Pricing Models with Heterogeneous Beliefs," MPRA Paper 1261, University Library of Munich, Germany.
    17. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
    18. Daniela Federici & Giancarlo Gandolfo, 2011. "The Euro/Dollar Exchange Rate: Chaotic or Non-Chaotic?," DEGIT Conference Papers c016_035, DEGIT, Dynamics, Economic Growth, and International Trade.
    19. Vishwesha Guttal & Srinivas Raghavendra & Nikunj Goel & Quentin Hoarau, 2016. "Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-20, January.
    20. Taisei Kaizoji, 2003. "Speculative bubbles and fat tail phenomena in a heterogeneous agent model," Papers nlin/0312040, arXiv.org.
    21. De Grauwe, Paul & Grimaldi, Marianna, 2006. "Exchange rate puzzles: A tale of switching attractors," European Economic Review, Elsevier, vol. 50(1), pages 1-33, January.
    22. Hammad A. Siddiqi, 2006. "Is it Social Influence on Beliefs Under Ambiguity? A Possible Explanation for Volatility Clustering," Microeconomics Working Papers 22279, East Asian Bureau of Economic Research.
    23. Daniela Federici & Giancarlo Gandolfo, 2011. "The Euro/Dollar Exchange Rate: Chaotic or Non-Chaotic?," DEGIT Conference Papers c016_035, DEGIT, Dynamics, Economic Growth, and International Trade.
    24. Hommes, C.H., 2005. "Heterogeneous Agents Models: two simple examples, forthcoming In: Lines, M. (ed.) Nonlinear Dynamical Systems in Economics, CISM Courses and Lectures, Springer, 2005, pp.131-164," CeNDEF Working Papers 05-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

    More about this item

    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:ams:ndfwpp:00-04. 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: (Cees C.G. Diks). General contact details of provider: http://edirc.repec.org/data/cnuvanl.html .

    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.