Dynamics of moving average rules in a continuous-time financial market model

Xue Zhong He*, Min Zheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used in discrete-time HAMs. The time delay represents a memory length of a moving average rule in discrete-time HAMs. Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize an otherwise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in financial markets.

Original languageEnglish
Pages (from-to)615-634
Number of pages20
JournalJournal of Economic Behavior and Organization
Issue number3
Publication statusPublished - Dec 2010
Externally publishedYes


  • Asset price
  • Bifurcations
  • Financial market behavior
  • Heterogeneous beliefs
  • Stability
  • Stochastic delay differential equations
  • Stylized facts


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