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An analysis of the effect of noise in a heterogeneous agent financial market model

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Author Info

  • Chiarella, Carl
  • He, Xue-Zhong
  • Zheng, Min

Abstract

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 35 (2011)
Issue (Month): 1 (January)
Pages: 148-162

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Handle: RePEc:eee:dyncon:v:35:y:2011:i:1:p:148-162

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Heterogeneous agents Speculative behaviour Stochastic bifurcations Stationary measures Chartists;

References

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  1. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  2. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "A dynamic analysis of moving average rules," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1729-1753.
  3. Charles M.C. Lee & Bhaskaran Swaminathan, 2000. "Price Momentum and Trading Volume," Journal of Finance, American Finance Association, vol. 55(5), pages 2017-2069, October.
  4. Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2003. "Evolutionary Stability of Portfolio Rules in Incomplete Markets," Discussion Papers 03-03, University of Copenhagen. Department of Economics.
  5. Peter Boswijk & Cars H. Hommes & Sebastiano Manzan, 2005. "Behavioral Heterogeneity in Stock Prices," Tinbergen Institute Discussion Papers 05-052/1, Tinbergen Institute.
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  7. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
  8. Cars Hommes & Florian Wagener, 2008. "Complex Evolutionary Systems in Behavioral Finance," Tinbergen Institute Discussion Papers 08-054/1, Tinbergen Institute.
  9. Horst, Ulrich & Rothe, Christian, 2008. "Queuing, Social Interactions, And The Microstructure Of Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 211-233, April.
  10. Brock,W.A. & Hommes,C.H., 2001. "Evolutionary dynamics in financial markets with many trader types," Working papers 7, Wisconsin Madison - Social Systems.
  11. Cees Diks & Florian Wagener, 2006. "A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems," Tinbergen Institute Discussion Papers 06-043/1, Tinbergen Institute.
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  13. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97.
  14. 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.
  15. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  16. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "Moving average rules as a source of market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 12-17.
  17. Rheinlaender Thorsten & Steinkamp Marcus, 2004. "A Stochastic Version of Zeeman's Market Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(4), pages 1-25, December.
  18. 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.
  19. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  20. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
  21. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May.
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  23. 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.
  24. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  25. 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.
  26. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
  27. Carl Chiarella & Xue-Zhong He & Min Zheng, 2007. "The Stochastic Dynamics of Speculative Prices," Research Paper Series 208, Quantitative Finance Research Centre, University of Technology, Sydney.
  28. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
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  30. 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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Citations

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Cited by:
  1. Fischer, Thomas, 2011. "News Reaction in Financial Markets within a Behavioral Finance Model with Heterogeneous Agents," Darmstadt Discussion Papers in Economics 54196, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
  2. Gregory Gagnon, 2012. "Exchange rate bifurcation in a stochastic evolutionary finance model," Decisions in Economics and Finance, Springer, vol. 35(1), pages 29-58, May.
  3. Carl Chiarella & Roberto Dieci & Xue-Zhong He & Kai Li, 2013. "An evolutionary CAPM under heterogeneous beliefs," Annals of Finance, Springer, vol. 9(2), pages 185-215, May.
  4. Yi Xue & Ramazan Gencay, 2009. "Hierarchical Information and the Rate of Information Diffusion," Working Paper Series 29_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  5. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2010. "Time-Varying Beta: A Boundedly Rational Equilibrium Approach," Research Paper Series 275, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
  7. Igor V. EVSTIGNEEVY & Thorsten HENS & Klaus Reiner SCHENK-HOPPE, . "An evolutionary financial market model with a risk-free asset," Swiss Finance Institute Research Paper Series 10-36, Swiss Finance Institute.

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