Adaptive Optimal Market Making Strategies with Inventory Liquidation Cos

TL;DR

This paper introduces a new high-frequency market-making strategy that adapts to order flow variability and general price dynamics, providing closed-form solutions and outperforming fixed strategies.

Contribution

It develops an adaptive, closed-form market-making model that accounts for demand randomness and general price processes, enhancing online responsiveness.

Findings

The adaptive strategy outperforms fixed and non-adaptive strategies in profit.

Model accurately reproduces P&L using real LOB data.

Demand variability significantly influences optimal order placement.

Abstract

A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand's randomness affects the optimal placement strategy. We also allow the price process to follow general dynamics without any Brownian or martingale assumption as is commonly adopted in the literature. The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using the actual flow of orders in the LOB. Our adaptive optimal strategies outperform the non-adaptive strategy and those that quote limit orders at a fixed distance from the midprice.