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A Dynamic Analysis of Speculation Across Two Markets

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Abstract

A discrete time model of a financial market is proposed, where the time evolution of asset prices and wealth arises from the interaction of two groups of agents, fundamentalists and chartists. Each group allocates its wealth between a risky asset (stock) and an alternative asset (bond), and the two groups have heterogeneous expectations about returns. We assume that chartists compute expected returns by extrapolating past price changes, while fundamentalists form their expectations on the basis of their superior knowledge of fundamentals. Under the assumption that agents have CRRA utility, investors' optimal demand for each asset depends on their wealth, and this results in growing price and wealth processes. The time evolution of the prices is modeled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an off-setting long or short position. The market maker is assumed to adjust the price, in each period, partly on the basis of the excess demand and partly according to a particular market stabilization policy. The model is reduced to a high dimensional nonlinear discrete-time dynamical system with growing prices and wealth. Although the model is nonstationary, suitable changes of variables lead to a stationary model where the dynamic variables are actual and expected returns, fundamental/price ratios, and wealth proportions of chartists and fundamentalists. The steady states and other invariant sets of the model are determined, and important global dynamic phenomena are studied via numerical techniques. Stochastic simulations are also performed, that show the ability of the model to generate some of the characteristic features of financial time series.

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  • Carl Chiarella & Roberto Dieci & Laura Gardini, 2003. "A Dynamic Analysis of Speculation Across Two Markets," Research Paper Series 89, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:89
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    1. 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.
    2. 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.
    3. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    4. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    5. 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.
    6. Madhavan, Ananth, 2000. "Market microstructure: A survey," Journal of Financial Markets, Elsevier, vol. 3(3), pages 205-258, August.
    7. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-248, May.
    8. 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.
    9. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    10. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(04), pages 503-536, September.
    11. Fernando Fernandez-Rodriguez & Maria-Dolores Garcia-Artiles & Juan Manuel Martin-Gonzalez, 2002. "A model of speculative behaviour with a strange attractor," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(3), pages 143-161.
    12. 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.
    13. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. 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.
    2. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, November.

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