We model trades-through, i.e. transactions that reach at least the second level of limit orders in an order book. Using tick-by-tick data on Euronext-traded stocks, we show that a simple bivariate Hawkes process fits nicely our empirical observations of trades-through. We show that the cross-influence of bid and ask trades-through is weak.
Hawkes processes limit order book trades-through highfrequency trading microstructure