Optimal trading of algorithmic orders in a liquidity fragmented market place

An optimization model for the execution of algorithmic orders at multiple trading venues is herein proposed and analyzed. The optimal trajectory consists of both market and limit orders, and takes advantage of any price or liquidity improvement in a particular market. The complexity of a multi-market environment poses a bi-level nonlinear optimization problem. The lower-level problem admits a unique solution thus enabling the second order conditions to be satisfied under a set of reasonable assumptions. The model is computationally affordable and solvable using standard software packages. The simulation results presented in the paper show the model's effectiveness using real trade data. From the outset, great effort was made to ensure that this was a challenging practical problem which also had a direct real world application. To be able to estimate in realtime the probability of fill for tens of thousands of orders at multiple price levels in a liquidity fragmented market place and finally carry out an optimization procedure to find the most optimal order placement solution is a significant computational breakthrough.