IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker

  • CHIARELLA, CARL
  • HE, XUE-ZHONG

This paper attempts to study the dynamics of a simple discounted present value asset price model where agents have different risk attitudes and follow different expectation formulation schemes for both first and second moments of the price distribution. Instead of using a Walrasian auctioneer scenario as the market clearing mechanism, a market maker scenario is used. In particular, the paper concentrates on models of fundamentalists and trend traders who follow least squares learning processes. An analysis is made of the effects of lag lengths on the stability of the fundamental equilibrium. Some necessary and/or sufficient conditions on the stability of the fundamental equilibrium associated with the speed of the adjustment of the market maker, different risk attitudes and different risk attitudes and different values of lags (used in the learning process) are established. The results lead to the following observations: (I) Compared with the findings with the Walrasian market clearing scenario in Brock and Hommes [8] and Chiarella and He [14], different price dynamics are obtained when the speed of the adjustment of the market maker increases and, in particular, when the contrarians are involved in the model; (ii) In contrast to homogeneous beliefs, where the larger is the lag length the more stable is that in general (for both the Walrasian and the market maker equilibrium) different lag lengths can complicate the price dynamics; (iii) In the model of trend followers versus contrarians, the stability of the fundamental equilibrium is determined by risk-adjusted aggregated extrapolation rates. This indicates that although every individual forecasting rule may lead to divergence from the equilibrium, these may "cancel out" in the aggregate and the actual dynamics with learning may thus be locally stable. On the other hand, only a small group of traders with expectation functions involving significant divergence can in fact destabilize the whole system.

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://journals.cambridge.org/abstract_S1365100502020114
File Function: link to article abstract page
Download Restriction: no

Article provided by Cambridge University Press in its journal Macroeconomic Dynamics.

Volume (Year): 7 (2003)
Issue (Month): 04 (September)
Pages: 503-536

as
in new window

Handle: RePEc:cup:macdyn:v:7:y:2003:i:04:p:503-536_02
Contact details of provider: Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK
Web page: http://journals.cambridge.org/jid_MDY
Email:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Bullard, James & Duffy, John, 1999. "Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs," Computational Economics, Society for Computational Economics, vol. 13(1), pages 41-60, February.
  2. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
  3. 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.
  4. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
  5. Day, R. & Huang, W., 1988. "Bulls, Bears And Market Sheep," Papers m8822, Southern California - Department of Economics.
  6. 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.
  7. Barucci, Emilio, 2001. "Fading memory learning in a class of forward-looking models with an application to hyperinflation dynamics," Economic Modelling, Elsevier, vol. 18(2), pages 233-252, April.
  8. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  9. Stoll, Hans R, 1978. "The Supply of Dealer Services in Securities Markets," Journal of Finance, American Finance Association, vol. 33(4), pages 1133-51, September.
  10. C. H. Hommes, 2001. "Financial markets as nonlinear adaptive evolutionary systems," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 149-167.
  11. Routledge, Bryan R, 1999. "Adaptive Learning in Financial Markets," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1165-1202.
  12. Chen, Shu-Heng & Yeh, Chia-Hsuan, 1997. "Toward a computable approach to the efficient market hypothesis: An application of genetic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1043-1063, June.
  13. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
  14. Franke, Reiner & Sethi, Rajiv, 1998. "Cautious trend-seeking and complex asset price dynamics," Research in Economics, Elsevier, vol. 52(1), pages 61-79, March.
  15. Garman, Mark B., 1976. "Market microstructure," Journal of Financial Economics, Elsevier, vol. 3(3), pages 257-275, June.
  16. 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 703-38, August.
  17. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
  18. Kaushik Mitra & Seppo Honkapohja, 1999. "Learning with Bounded Memory in Stochastic Models," Computing in Economics and Finance 1999 221, Society for Computational Economics.
  19. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
  20. Peck, James, 1990. "Liquidity without money: A General equilibrium model of market microstructure," Journal of Financial Intermediation, Elsevier, vol. 1(1), pages 80-103, March.
  21. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
  22. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  23. 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.
  24. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  25. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
  26. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute.
  27. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
  28. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
  29. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  30. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute.
  31. Kyle, Albert & Campbell, John, 1993. "Smart Money, Noise Trading and Stock Price Behaviour," Scholarly Articles 3208217, Harvard University Department of Economics.
  32. 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.
  33. Balasko, Yves & Royer, Daniel, 1996. "Stability of Competitive Equilibrium with Respect to Recursive and Learning Processes," Journal of Economic Theory, Elsevier, vol. 68(2), pages 319-348, February.
  34. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
  35. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-68, September.
  36. James Bullard, 1991. "Learning equilibria," Working Papers 1991-004, Federal Reserve Bank of St. Louis.
  37. 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.
  38. 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.
  39. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
  40. Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
  41. repec:att:wimass:9706 is not listed on IDEAS
  42. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cup:macdyn:v:7:y:2003:i:04:p:503-536_02. 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: (Keith Waters)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.