  We provide some theoretical extensions and a calibration protocol for our
former dynamic optimal execution model. The Hawkes parameters and the
propagator are estimated independently on financial data from stocks of the
CAC40. Interestingly, the propagator exhibits a smoothly decaying form with one
or two dominant time scales, but only so after a few seconds that the market
needs to adjust after a large trade. Motivated by our estimation results, we
derive the optimal execution strategy for a multi-exponential Hawkes kernel and
backtest it on the data for round trips. We find that the strategy is
profitable on average when trading at the midprice, which is in accordance with
violated martingale conditions. However, in most cases, these profits vanish
when we take bid-ask costs into account.
