Optimal split of orders across liquidity pools: a stochastic algorithm approach

TL;DR

This paper introduces two stochastic recursive algorithms for optimally splitting large orders across multiple liquidity pools, with proven convergence and performance analysis on simulated and real trading data.

Contribution

It develops and analyzes two novel stochastic algorithms for order splitting, providing theoretical convergence proofs and empirical performance comparisons.

Findings

Algorithms converge almost surely under mild conditions

Convergence rate follows a Central Limit Theorem for i.i.d. inputs

Performance surpasses naive strategies in simulations and real data

Abstract

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.