Optimal Execution Strategies Incorporating Internal Liquidity Through Market Making

TL;DR

This work extends the Cartea et al. optimal execution framework by incorporating internal liquidity from market making alongside interbank limit and market orders. The model applies combined stochastic-impulse control to derive a Hamilton-Jacobi-Bellman Quasi-Variational Inequality, which is solved numerically to obtain optimal LO depth, MM spread, MO sizes, and MO timing. A key finding is that internal MM liquidity can be leveraged to reduce external market impact while informing dynamic trade-offs between liquidity sources, as demonstrated through Finite Difference Method solutions and comparative benchmarks. The approach provides a practical framework for executing large orders in OTC markets by balancing interbank and internal liquidity to improve execution efficiency and risk management.

Abstract

This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{cartea2015algorithmic} framework, we incorporate market impact in interbank orders while excluding it for internal market-making transactions. Our model aims to optimize the balance between interbank and internal liquidity, reducing market impact and improving execution efficiency.

Figures (3)

• Figure 1: Image of algorithm execution utilizing MM
• Figure 2: Optimal execution schdule and MO timing
• Figure 3: Optimal spread $\delta^I$ and depth $\delta^L$