Market making under a weakly consistent limit order book model

Abstract

We develop a new market‐making model, from the ground up, which is tailored toward high‐frequency trading under a limit order book (LOB), based on the well‐known classification of order types in market microstructure. Our flexible framework allows arbitrary order volume, price jump, and bid‐ask spread distributions as well as the use of market orders. It also honors the consistency of price movements upon arrivals of different order types. For example, it is apparent that prices should never go down on buy market orders. In addition, it respects the price‐time priority of LOB. In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov (Quantitative Finance, 8, 217, 2008) market‐making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order book features. The Hamilton‐Jacobi‐Bellman quasi‐variational inequality (HJBQVI) associated with the control problem can be solved numerically via finite‐difference method. We illustrate our optimal trading strategy with a full numerical analysis, calibrated to the order book statistics of a popular exchanged‐traded fund (ETF). Our simulation shows that the profit of market‐making can be severely overstated under LOBs with inconsistent price movements.

Deep Reinforcement Learning in Cryptocurrency Market Making

“…There has been ample research in modeling the LOB using statistical, machine learning, and deep learning approaches. [2,7,13,22] use a marked point process to indirectly predict midpoint price changes and inventory control for market making. [24] use order flow imbalances and linear regressions to predict midpoint changes.…”

“…Exchange market makers facilitate transactions amongst participants by providing liquidity in the LOB. Traditionally, statistical approaches have been used to model limit order books for market making and inventory control optimization [2,7]. Understanding that there have been many recent advancements in deep reinforcement learning in other domains such as video games [10,14], yet very little research published on the application of deep reinforcement learning to market making, the focus of this paper is to apply deep reinforcement to cryptocurrency market making.…”

Deep Reinforcement Learning for Market Making Under a Hawkes Process-Based Limit Order Book Model

“…Regardless of the approach used, faithful LOB modeling, ideally accounting for the empirical properties and stylized facts of market microstructure as well as the discrete nature of the LOB itself, is pivotal to obtaining high-performing MM controllers. However, due to the naive assumptions they are predicated upon, the LOB models underlying most contemporary MM approaches remain inconsistent with respect to direction, timing, and volume, leading to phantom gains under backtesting and preposterous events [16], such as price decreases after a large buy market order. For example, in the original AS model [1], price movements are assumed to be completely independent of the arrivals of market orders and the LOB dynamics, while the subsequent approaches only partly address such inconsistencies.…”

“…For example, in the original AS model [1], price movements are assumed to be completely independent of the arrivals of market orders and the LOB dynamics, while the subsequent approaches only partly address such inconsistencies. To ameliorate this, a novel weakly-consistent pure-jump market model that ensures that the price dynamics are consistent with the LOB dynamics with respect to direction and timing is proposed in [16]. Nevertheless, it still assumes constant order arrival intensities, meaning that any (empirically found) effects of self-or mutualexcitation and inhibition between various types of LOB order arrivals remain unaccounted for.…”

Reinforcement Learning Approaches to Optimal Market Making

“…Most analytical approaches follow a similar recipe, deriving (near-)optimal strategies via the use of a system of differential equations underpinning the assumed model. However, such models (1) are typically predicated upon a set of strong, naive assumptions, (2) employ multiple parameters that need to be laboriously calibrated on historical market data, and (3) fail to properly take into account the market microstructure dynamics, especially by assuming inconsistent limit order book models [2]. For example, the AS model assumes that the reference price follows a driftless diffusion process, that the intensities at which the market maker's limit orders become filled only depend on the distance from the reference price, and that the order arrivals and the reference price are completely independent, all of which are proven not to be reliable assumptions.…”