We consider an agent-based model of financial markets with asynchronous order arrival in continuous time. Buying and selling orders arrive in accordance with a Poisson dynamics where the order rates depend both on past prices and on the mood of the market. The agents form their demand for an asset on the basis of their forecasts of future prices and their forecasting rules may change over time as a result of the influence of other traders. Among the possible rules are “chartist” or extrapolatory rules. We prove that when chartists are in the market, and with choice of scaling, the dynamics of asset prices can be approximated by an ordinary delay differential equation. The fluctuations around the first-order approximation follow an Ornstein–Uhlenbeck dynamics with delay in a random environment of investor sentiment.
