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Heterogeneous Beliefs and Adaptive Behaviour in a Continuous-Time Asset Price Model

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Abstract

This paper extends the analysis of the seminal paper of Brock and Hommes (1998) on heterogeneous beliefs and routes to chaos in a simple asset price model in discrete-time to a model in continuous-time. The resulting model characterized mathematically by a system of stochastic delay differential equations provides a unified approach to deal with adaptive behaviour of heterogeneous agents and stability impact of lagged price information used by chartists to form their expectations. For the underlyingd eterministic model, we show not only that the result of Brock and Hommes on rational routes to market instability in discrete-time holds in continuous time but also a double edged effect of an increase in lagged price information used by the chartists on market stability. For the stochastic model, we demonstrate that the model is able to display various market phenomena such as bubbles and crashes and replicate stylized facts including volatility clustering, and long range dependence in volatility.

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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 291.

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Length: 25
Date of creation: 01 Jun 2011
Date of revision:
Handle: RePEc:uts:rpaper:291

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Keywords: heterogeneous beliefs; bounded rationality; adaptiveness; fundamentalists; chartists; stability; stochastic delay differential equations;

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References

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  1. Chiarella, C. & He, X.-Z. & Hommes, C.H., 2004. "A Dynamic Analysis of Moving Average Rules," CeNDEF Working Papers 04-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  2. Anufriev, Mikhail & Dindo, Pietro, 2010. "Wealth-driven selection in a financial market with heterogeneous agents," Journal of Economic Behavior & Organization, Elsevier, vol. 73(3), pages 327-358, March.
  3. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
  4. Xue-Zhong He & Min Zheng, 2010. "Dynamics of Moving Average Rules in a Continuous-time Financial Market Model," Research Paper Series 268, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. William A. Brock & Cars H. Hommes, 1995. "Rational Routes to Randomness," Working Papers 95-03-029, Santa Fe Institute.
  6. Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics.
  7. Carl Chiarella & Roberto Dieci & Laura Gardini, 2005. "The Dynamic Interaction of Speculation and Diversification," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 17-52.
  8. Xue-Zhong He & Kai Li & Junjie Wei & Min Zheng, 2009. "Market Stability Switches in a Continuous-Time Financial Market with Heterogeneous Beliefs," Research Paper Series 252, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Carl Chiarella & Xue-Zhong He, 2001. "Dynamics of Beliefs and Learning Under aL Processes - The Heterogeneous Case," Research Paper Series 55, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. 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.
  11. Carl Chiarella & Xue-Zhong He, 2000. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker," Research Paper Series 35, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Society for Computational Economics, vol. 26(1), pages 19-49, August.
  13. 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.
  14. Carl Chiarella & Roberto Dieci & Laura Gardini, 2001. "Speculative Behaviour and Complex Asset Price Dynamics," Research Paper Series 49, Quantitative Finance Research Centre, University of Technology, Sydney.
  15. Day, R. & Huang, W., 1988. "Bulls, Bears And Market Sheep," Papers m8822, Southern California - Department of Economics.
  16. repec:att:wimass:9621 is not listed on IDEAS
  17. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
  18. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October.
  19. 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.
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