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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.

Suggested Citation

  • Xue-Zhong He & Kai Li, 2011. "Heterogeneous Beliefs and Adaptive Behaviour in a Continuous-Time Asset Price Model," Research Paper Series 291, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:291
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    More about this item

    Keywords

    heterogeneous beliefs; bounded rationality; adaptiveness; fundamentalists; chartists; stability; stochastic delay differential equations;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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