Revisiting Trade-sign Long-memory and Square-root Law price impact (opens in new tab)

Starting with a coupled discrete reaction--diffusion formulation for the lit and latent order books with non-uniformly sampled event times and meta-order source terms we show how two familiar market-microstructure regularities can emerge from this framework: the long-memory of trade signs associated with the Lillo--Mike--Farmer (LMF) theory and the square-root law (SQRL) of meta-order impact. This uses the well known locally linear order book an...