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We describe an agent-based model where trading occurs in event-based time called directional-change intrinsic time [Guillaume et al., 1997]. This time is endogenously defined and it ticks when the price makes a reversal of a certain threshold from the local extreme. Intrinsic events dissect the price curve into directional-changes and overshoots. Average overshoot length of both empirical and theoretical time series exhibit a stable pattern that holds over several orders of magnitude called scaling law. The overshoot scaling law states that on average the overshoot approximately equals the size of the directional-change which was found to be an omnipresent feature of all liquid markets [Glattfelder et al., 2011]. The developed model serves as a complex system, populated by a large number of independent and heterogeneous agents with unique properties and trading patterns. All trades have the same fixed volume and the price impact of the traded net volume is modeled according to the empirically observed squared root impact function [Bouchaud, 2010]. The time series generated by the model reproduces four traditional stylized facts of foreign exchange rates: low auto-correlation of returns, fat-tailed distribution of returns, aggregational normality, mean price move scaling law. In addition, the agent-based model also replicates the overshoot scaling law. The trend of the generated time series depends on the set of selected agents with specific thresholds. The main advantage of the model is that despite its simplicity it replicates properties of time series reflecting the behavior of very sophisticated market participants with a diverse range of tactics and regimes.
[Bouchaud, 2010] Bouchaud, J.-P. (2010). Price impact. Encyclopedia of quantitative finance.
[Glattfelder et al., 2011] Glattfelder, J., Dupuis, A., and Olsen, R. (2011). Patterns in high-frequency fx data: discovery of 12 empirical scaling laws. Quantitative Finance, 11(4):599–614.
[Guillaume et al., 1997] Guillaume, D. M., Dacorogna, M. M., Dav ́e, R. R., M ̈uller, U. A., Olsen, R. B., and Pictet, O. V. (1997). From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Finance and stochastics, 1(2):95–129.
