Market Microstructure

Adaptive Curves for Optimally Efficient Market Making ArXiv ID: 2406.13794 “View on arXiv” Authors: Unknown Abstract Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bonding curves to trader behavior, based on the classical market microstructure model of Glosten and Milgrom. Our approach ensures a zero-profit condition for the market maker’s prices. We derive the differential equation that an optimal adaptive curve should follow to minimize arbitrage losses while remaining competitive. Solutions to this optimality equation are obtained for standard Gaussian and Lognormal price models using Kalman filtering. A key feature of our method is its ability to estimate the external market price without relying on price or loss oracles. We also provide an equivalent differential equation for the implied dynamics of canonical static bonding curves and establish conditions for their optimality. Our algorithms demonstrate robustness to changing market conditions and adversarial perturbations, and we offer an on-chain implementation using Uniswap v4 alongside off-chain AI co-processors. ...

Heterogeneous Beliefs Model of Stock Market Predictability ArXiv ID: 2406.08448 “View on arXiv” Authors: Unknown Abstract This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset’s fundamental value through a noisy signal. The investors are heterogeneous in that they have different beliefs about the stochastic supply. A momentum in the stock price arises from those agents who incorrectly underestimate the signal accuracy, dampening the initial price impact of the signal. A reversal in price occurs because the price reverts to the fundamental value in the long run. An extension of the model to multiple assets case predicts co-movement and lead-lag effect, in addition to cross-sectional momentum and reversal. The heterogeneous beliefs of investors about news demonstrate how the main predictability anomalies arise endogenously in a model of bounded rationality. ...

An Algebraic Framework for the Modeling of Limit Order Books ArXiv ID: 2406.04969 “View on arXiv” Authors: Unknown Abstract Introducing an algebraic framework for modeling limit order books (LOBs) with tools from physics and stochastic processes, our proposed framework captures the creation and annihilation of orders, order matching, and the time evolution of the LOB state. It also enables compositional settings, accommodating the interaction of heterogeneous traders and different market structures. We employ Dirac notation and generalized generating functions to describe the state space and dynamics of LOBs. The utility of this framework is shown through simulations of simplified market scenarios, illustrating how variations in trader behavior impact key market observables such as spread, return volatility, and liquidity. The algebraic representation allows for exact simulations using the Gillespie algorithm, providing a robust tool for exploring the implications of market design and policy changes on LOB dynamics. Future research can expand this framework to incorporate more complex order types, adaptive event rates, and multi-asset trading environments, offering deeper insights into market microstructure and trader behavior and estimation of key drivers for market microstructure dynamics. ...

Modelling financial volume curves with hierarchical Poisson processes ArXiv ID: 2406.19402 “View on arXiv” Authors: Unknown Abstract Modeling the trading volume curves of financial instruments throughout the day is of key interest in financial trading applications. Predictions of these so-called volume profiles guide trade execution strategies, for example, a common strategy is to trade a desired quantity across many orders in line with the expected volume curve throughout the day so as not to impact the price of the instrument. The volume curves (for each day) are naturally grouped by stock and can be further gathered into higher-level groupings, such as by industry. In order to model such admixtures of volume curves, we introduce a hierarchical Poisson process model for the intensity functions of admixtures of inhomogenous Poisson processes, which represent the trading times of the stock throughout the day. The model is based on the hierarchical Dirichlet process, and an efficient Markov Chain Monte Carlo (MCMC) algorithm is derived following the slice sampling framework for Bayesian nonparametric mixture models. We demonstrate the method on datasets of different stocks from the Trade and Quote repository maintained by Wharton Research Data Services, including the most liquid stock on the NASDAQ stock exchange, Apple, demonstrating the scalability of the approach. ...

A Novel Approach to Queue-Reactive Models: The Importance of Order Sizes ArXiv ID: 2405.18594 “View on arXiv” Authors: Unknown Abstract In this article, we delve into the applications and extensions of the queue-reactive model for the simulation of limit order books. Our approach emphasizes the importance of order sizes, in conjunction with their type and arrival rate, by integrating the current state of the order book to determine, not only the intensity of order arrivals and their type, but also their sizes. These extensions generate simulated markets that are in line with numerous stylized facts of the market. Our empirical calibration, using futures on German bonds, reveals that the extended queue-reactive model significantly improves the description of order flow properties and the shape of queue distributions. Moreover, our findings demonstrate that the extended model produces simulated markets with a volatility comparable to historical real data, utilizing only endogenous information from the limit order book. This research underscores the potential of the queue-reactive model and its extensions in accurately simulating market dynamics and providing valuable insights into the complex nature of limit order book modeling. ...

“Microstructure Modes” – Disentangling the Joint Dynamics of Prices & Order Flow ArXiv ID: 2405.10654 “View on arXiv” Authors: Unknown Abstract Understanding the micro-dynamics of asset prices in modern electronic order books is crucial for investors and regulators. In this paper, we use an order by order Eurostoxx database spanning over 3 years to analyze the joint dynamics of prices and order flow. In order to alleviate various problems caused by high-frequency noise, we propose a double coarse-graining procedure that allows us to extract meaningful information at the minute time scale. We use Principal Component Analysis to construct “microstructure modes” that describe the most common flow/return patterns and allow one to separate them into bid-ask symmetric and bid-ask anti-symmetric. We define and calibrate a Vector Auto-Regressive (VAR) model that encodes the dynamical evolution of these modes. The parameters of the VAR model are found to be extremely stable in time, and lead to relatively high $R^2$ prediction scores, especially for symmetric liquidity modes. The VAR model becomes marginally unstable as more lags are included, reflecting the long-memory nature of flows and giving some further credence to the possibility of “endogenous liquidity crises”. Although very satisfactory on several counts, we show that our VAR framework does not account for the well known square-root law of price impact. ...

Data-driven measures of high-frequency trading ArXiv ID: 2405.08101 “View on arXiv” Authors: Unknown Abstract High-frequency trading (HFT) accounts for almost half of equity trading volume, yet it is not identified in public data. We develop novel data-driven measures of HFT activity that separate strategies that supply and demand liquidity. We train machine learning models to predict HFT activity observed in a proprietary dataset using concurrent public intraday data. Once trained on the dataset, these models generate HFT measures for the entire U.S. stock universe from 2010 to 2023. Our measures outperform conventional proxies, which struggle to capture HFT’s time dynamics. We further validate them using shocks to HFT activity, including latency arbitrage, exchange speed bumps, and data feed upgrades. Finally, our measures reveal how HFT affects fundamental information acquisition. Liquidity-supplying HFTs improve price discovery around earnings announcements while liquidity-demanding strategies impede it. ...

High-Frequency Stock Market Order Transitions during the US-China Trade War 2018: A Discrete-Time Markov Chain Analysis ArXiv ID: 2405.05634 “View on arXiv” Authors: Unknown Abstract Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the USA-China trade war of 2018. The Markov property of the order sequence is validated by the Chi-square test. We estimate the transition probability matrix of the sequence using maximum likelihood estimation. From the heat-map of these matrices, we found the presence of active participation by different types of traders during high volatility days. On such days, these traders place limit orders primarily with the intention of deleting the majority of them to influence the market. These findings are supported by high stationary distribution and low mean recurrence values of add and delete orders. Further, we found similar spectral gap and entropy rate values, which indicates that similar trading strategies are employed on both high and low volatility days during the trade war. Among all the sectors considered in this study, we observe that there is a recurring pattern of full execution orders in Finance & Banking sector. This shows that the banking stocks are resilient during the trade war. Hence, this study may be useful in understanding stock market order dynamics and devise trading strategies accordingly on high and low volatility days during extreme macroeconomic events. ...

Non cooperative Liquidity Games and their application to bond market trading ArXiv ID: 2405.02865 “View on arXiv” Authors: Unknown Abstract We present a new type of game, the Liquidity Game. We draw inspiration from the UK government bond market and apply game theoretic approaches to its analysis. In Liquidity Games, market participants (agents) use non-cooperative games where the players’ utility is directly defined by the liquidity of the game itself, offering a paradigm shift in our understanding of market dynamics. Each player’s utility is intricately linked to the liquidity generated within the game, making the utility endogenous and dynamic. Players are not just passive recipients of utility based on external factors but active participants whose strategies and actions collectively shape and are shaped by the liquidity of the market. This reflexivity introduces a level of complexity and realism previously unattainable in conventional models. We apply Liquidity Game theoretic approaches to a simple UK bond market interaction and present results for market design and strategic behavior of participants. We tackle one of the largest issues within this mechanism, namely what strategy should market makers utilize when uncertain about the type of market maker they are interacting with, and what structure might regulators wish to see. ...

Quantifying Price Improvement in Order Flow Auctions ArXiv ID: 2405.00537 “View on arXiv” Authors: Unknown Abstract This work introduces a framework for evaluating onchain order flow auctions (OFAs), emphasizing the metric of price improvement. Utilizing a set of open-source tools, our methodology systematically attributes price improvements to specific modifiable inputs of the system such as routing efficiency, gas optimization, and priority fee settings. When applied to leading Ethereum-based trading interfaces such as 1Inch and Uniswap, the results reveal that auction-enhanced interfaces can provide statistically significant improvements in trading outcomes, averaging 4-5 basis points in our sample. We further identify the sources of such price improvements to be added liquidity for large swaps. This research lays a foundation for future innovations in blockchain based trading platforms. ...