Clustering of order arrivals, price impact and trade path optimisation

We fit a bivariate Hawkes process to arrival data for buy and sell trades in FX markets. The model can be used to predict future imbalance of buy and sell trades conditional on history of recent trade arrivals. We derive formulae for the raw price impact of a trade as a function of time assuming that trade arrivals are governed by a Hawkes process and that the price is a martingale, and show that the price impact of a series of trades is given by superposition of their individual price impacts. We use these formulae to parameterise a model for optimal liquidation strategies.