Extension and calibration of a Hawkes-based optimal execution model

TL;DR

This paper extends a Hawkes-based optimal execution model with theoretical developments and calibration on CAC40 stock data, deriving a strategy that is profitable before costs but not after considering bid-ask spreads.

Contribution

It introduces a calibrated multi-exponential Hawkes kernel model and derives an optimal execution strategy based on empirical data.

Findings

Propagator shows a smoothly decaying form with dominant time scales

Optimal strategy is profitable before costs when trading at midprice

Profits vanish when bid-ask costs are included

Abstract

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.