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Asset price and wealth dynamics in a financial market with heterogeneous agents

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  • Carl Chiarella
  • Roberto Dieci

Abstract

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics is determined by the interaction of two groups of agents, fundamentalists and trend extrapolators. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the risky return over the next period. We assume that investors have CRRA utility, so that their optimal demands for each asset depend on their wealth. A market maker is assumed to adjust the price at the end of each trading period, on the basis of the excess demand. The model results in a high dimensional nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the market dynamics is highly dependent on the parameters which characterize agents" behavior and that in some cases a “fundamental†steady state coexists with other steady states or different attractors. In such cases, the role played by the initial condition (in particular the initial wealth shares) is analyzed in detail by means of numerical investigation of the basins of attraction

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 261.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:261

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Keywords: Heterogeneous beliefs; asset pricing; wealth dynamics; global dynamics; basins of attraction;

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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. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233 Elsevier.
  3. William A. Brock & Blake D. LeBaron, 1995. "A Dynamic Structural Model for Stock Return Volatility and Trading Volume," NBER Working Papers 4988, National Bureau of Economic Research, Inc.
  4. Hommes, Cars & Huang, Hai & Wang, Duo, 2005. "A robust rational route to randomness in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1043-1072, June.
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  6. Thorsten Hens & Klaus Reiner Schenk-Hoppé, . "Markets Do Not Select For a Liquidity Preference as Behavior Towards Risk," IEW - Working Papers 139, Institute for Empirical Research in Economics - University of Zurich.
  7. 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.
  8. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
  9. Chen, Shu-Heng & Yeh, Chia-Hsuan, 2002. "On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 217-239, October.
  10. 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.
  11. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  12. Madhavan, Ananth & Smidt, Seymour, 1993. " An Analysis of Changes in Specialist Inventories and Quotations," Journal of Finance, American Finance Association, vol. 48(5), pages 1595-1628, December.
  13. 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.
  14. 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.
  15. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
  16. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, October.
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  18. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  19. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
  20. 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.
  21. Madhavan, Ananth, 2000. "Market microstructure: A survey," Journal of Financial Markets, Elsevier, vol. 3(3), pages 205-258, August.
  22. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
  23. Carl Chiarella & Xue-Zhong He, 2002. "An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies," Research Paper Series 84, Quantitative Finance Research Centre, University of Technology, Sydney.
  24. 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.
  25. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2002. "Speculative behaviour and complex asset price dynamics: a global analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 173-197, October.
  26. 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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