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Bifurcation Routes to Volatility Clustering

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Author Info
Andrea Gaunersdorfer (University of Vienna)
Cars Hommes ()
Florian O.O. Wagener () (University of Amsterdam)

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Abstract

A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically in nonlinear multi-agent evolutionary systems.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-015/1.

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Date of creation: 06 Feb 2001
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Handle: RePEc:dgr:uvatin:20010015

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  1. Orlando Gomes, . "Volatility, Heterogeneous Agents and Chaos," The Electronic Journal of Evolutionary Modeling and Economic Dynamics, IFReDE - Université Montesquieu Bordeaux IV. [Downloadable!]
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  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
  4. Boer-Sorban, K. & Kaymak, U. & Bruin, A. de, 2005. "A Modular Agent-Based Environment for Studying Stock Markets," Research Paper ERS-2005-017-LIS Revision, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni. [Downloadable!]
  5. repec:att:wimass:192017 is not listed on IDEAS
  6. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2003. "Bifurcation Routes to Volatility Clustering under Evolutionary Learning," CeNDEF Working Papers 03-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
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  7. Roberto Dieci & Ilaria Foroni & Laura Gardini & Xue-Zhong He, 2005. "Market Mood, Adaptive Beliefs and Asset Price Dynamics," Research Paper Series 162, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  8. Siddiqi, Hammad, 2007. "Rational Interacting Agents and Volatility Clustering: A New Approach," MPRA Paper 2984, University Library of Munich, Germany. [Downloadable!]
  9. 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. [Downloadable!]
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  10. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "A Behavioural Asset Pricing Model with a Time-Varying Second Moment," Research Paper Series 141, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  11. Jean-Michel Grandmont, 2008. "Nonlinear Difference Equations, Bifurcations and Chaos: An Introduction," Working Papers 2008_23, University of Venice "Ca' Foscari", Department of Economics. [Downloadable!]
  12. 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. [Downloadable!]
  13. S. Borovkova & H. Dehling & J. Renkema & H. Tulleken, 2003. "A Potential-Field Approach to Financial Time Series Modelling," Computational Economics, Springer, vol. 22(2), pages 139-161, October. [Downloadable!] (restricted)
  14. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2002. "Evolutionary dynamics in markets with many trader types," CeNDEF Working Papers 02-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
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  15. Henrik Amilon, 2003. "Estimation of an Adaptive Stock Market Model with Heterogeneous Agents," Research Paper Series 107, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  16. Andrea Morone, 2005. "Financial Market in the Laboratory, an Experimental Analysis of some Stylized Facts," Papers on Strategic Interaction 2005-27, Max Planck Institute of Economics, Strategic Interaction Group. [Downloadable!]
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  17. Carl Chiarella & Xue-Zhong He, 2001. "Asset Price and Wealth Dynamics Under Heterogeneous Expectations," Research Paper Series 56, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  18. Alfarano, Simone & Lux, Thomas, 2005. "A noise trader model as a generator of apparent financial power laws and long memory," Economics Working Papers 2005,13, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
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  19. De Grauwe, Paul & Grimaldi, Marianna, 2004. "Exchange Rate Puzzles: A Tale of Switching Attractors," Working Paper Series 163, Sveriges Riksbank (Central Bank of Sweden). [Downloadable!]
  20. Ilaria Foroni & Anna Agliari, 2008. "Complex Price Dynamics in a Financial Market with Imitation," Computational Economics, Springer, vol. 32(1), pages 21-36, September. [Downloadable!] (restricted)
  21. Taisei Kaizoji, 2003. "Speculative bubbles and fat tail phenomena in a heterogeneous agent model," Quantitative Finance Papers nlin/0312040, arXiv.org. [Downloadable!]
  22. Verbic, Miroslav, 2006. "Memory and Asset Pricing Models with Heterogeneous Beliefs," MPRA Paper 1261, University Library of Munich, Germany. [Downloadable!]
  23. Amilon, Henrik, 2005. "Estimation of an Adaptive Stock Market Model with Heterogeneous Agents," Working Paper Series 177, Sveriges Riksbank (Central Bank of Sweden). [Downloadable!]
  24. Siddiqi, Hammad, 2006. "Belief merging and revision under social influence: An explanation for the volatility clustering puzzle," MPRA Paper 657, University Library of Munich, Germany. [Downloadable!]
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