Agent-Based Model in Directional-Change Intrinsic Time

We describe an agent-based model where trades happen in event-based time called directional-change intrinsic time. Events are defined as the reversal price moves of a directional-change threshold from a local extreme. The price impact of traded volumes is modelled according to the empirically observed squared root impact function. The time series generated by the agents is characterised by statistical properties typical for foreign exchange rates: low auto-correlation of returns, fat-tailed distribution of returns, aggregated normality, and the price jump scaling law. Furthermore, we introduce and use as a benchmark, the overshoot scaling law, which is an omnipresent feature of liquid markets and relates the expected length of price overshoots to the length of the corresponding directional-change threshold