Market Microstructure

Strategic Learning and Trading in Broker-Mediated Markets ArXiv ID: 2412.20847 “View on arXiv” Authors: Unknown Abstract We study strategic interactions in a broker-mediated market. A broker provides liquidity to an informed trader and to noise traders while managing inventory in the lit market. The broker and the informed trader maximise their trading performance while filtering each other’s private information; the trader estimates the broker’s trading activity in the lit market while the broker estimates the informed trader’s private signal. Brokers hold a strategic advantage over traders who rely solely on prices to filter information. We find that information leakage in the client’s trading flow yields an economic value to the broker that is comparable to transaction costs; she speculates profitably and mitigates risk effectively, which, in turn, adversely impacts the informed trader’s performance. In contrast, low signal-to-noise sources, such as prices, result in the broker’s trading performance being indistinguishable from that of a naive strategy that internalises noise flow, externalises informed flow, and offloads inventory at a constant rate. ...

A mathematical framework for modelling CLMM dynamics in continuous time ArXiv ID: 2412.18580 “View on arXiv” Authors: Unknown Abstract This paper develops a rigorous mathematical framework for analyzing Concentrated Liquidity Market Makers (CLMMs) in Decentralized Finance (DeFi) within a continuous-time setting. We model the evolution of liquidity profiles as measure-valued processes and characterize their dynamics under continuous trading. Our analysis encompasses two critical aspects of CLMMs: the mechanics of concentrated liquidity provision and the strategic behavior of arbitrageurs. We examine three distinct arbitrage models – myopic, finite-horizon, and infinite-horizon with discounted and ergodic controls – and derive closed-form solutions for optimal arbitrage strategies under each scenario. Importantly, we demonstrate that the presence of trading fees fundamentally constrains the admissible price processes, as the inclusion of fees precludes the existence of diffusion terms in the price process to avoid infinite fee generation. This finding has significant implications for CLMM design and market efficiency. ...

Broker-Trader Partial Information Nash-Equilibria ArXiv ID: 2412.17712 “View on arXiv” Authors: Unknown Abstract We study partial information Nash equilibrium between a broker and an informed trader. In this setting, the informed trader, who possesses knowledge of a trading signal, trades multiple assets with the broker in a dealer market. Simultaneously, the broker offloads these assets in a lit exchange where their actions impact the asset prices. The broker, however, only observes aggregate prices and cannot distinguish between underlying trends and volatility. Both the broker and the informed trader aim to maximize their penalized expected wealth. Using convex analysis, we characterize the Nash equilibrium and demonstrate its existence and uniqueness. Furthermore, we establish that this equilibrium corresponds to the solution of a nonstandard system of forward-backward stochastic differential equations (FBSDEs) that involves the two differing filtrations. For short enough time horizons, we prove that a unique solution of this system exists. Finally, under quite general assumptions, we show that the solution to the FBSDE system admits a polynomial approximation in the strength of the transient impact to arbitrary order, and prove that the error is controlled. ...

Expressions of Market-Based Correlations Between Prices and Returns of Two Assets ArXiv ID: 2412.13172 “View on arXiv” Authors: Unknown Abstract This paper derives the expressions of correlations between prices of two assets, returns of two assets, and price-return correlations of two assets that depend on statistical moments and correlations of the current values, past values, and volumes of their market trades. The usual frequency-based expressions of correlations of time series of prices and returns describe a partial case of our model when all trade volumes and past trade values are constant. Such an assumptions are rather far from market reality, and its use results in excess losses and wrong forecasts. Traders, banks, and funds that perform multi-million market transactions or manage billion-valued portfolios should consider the impact of large trade volumes on market prices and returns. The use of the market-based correlations of prices and returns of two assets is mandatory for them. The development of macroeconomic models and market forecasts like those being created by BlackRock’s Aladdin, JP Morgan, and the U.S. Fed., is impossible without the use of market-based correlations of prices and returns of two assets. ...

Auto-Regressive Control of Execution Costs ArXiv ID: 2412.10947 “View on arXiv” Authors: Unknown Abstract Bertsimas and Lo’s seminal work established a foundational framework for addressing the implementation shortfall dilemma faced by large institutional investors. Their models emphasized the critical role of accurate knowledge of market microstructure and price/information dynamics in optimizing trades to minimize execution costs. However, this paper recognizes that perfect initial knowledge may not be a realistic assumption for new investors entering the market. Therefore, this study aims to bridge this gap by proposing an approach that iteratively derives OLS estimates of the market parameters from period to period. This methodology enables uninformed investors to engage in the market dynamically, adjusting their strategies over time based on evolving estimates, thus offering a practical solution for navigating the complexities of execution cost optimization without perfect initial knowledge. ...

Stochastic Gradient Descent in the Optimal Control of Execution Costs ArXiv ID: 2412.12199 “View on arXiv” Authors: Unknown Abstract Bertsimas and Lo’s seminal work laid the groundwork for addressing the implementation shortfall dilemma in institutional investing, emphasizing the significance of market microstructure and price dynamics in minimizing execution costs. However, the ability to derive a theoretical Optimum market order policy is an unrealistic assumption for many investors. This study aims to bridge this gap by proposing an approach that leverages stochastic gradient descent (SGD) to derive alternative solutions for optimizing execution cost policies in dynamic markets where explicit mathematical solutions may not yet exist. The proposed methodology assumes the existence of a mathematically derived optimal solution that is a function of the underlying market dynamics. By iteratively refining strategies using SGD, economists can adapt their approaches over time based on evolving execution strategies. While these SGD-based solutions may not achieve optimality, they offer valuable insights into optimizing policies under complex market frameworks. These results serve as a bridge for economists and mathematicians, facilitating the study of the Optimum policy volatile markets while offering SGD driven implementable policies that closely approximate optimal outcomes within shorter time frames. ...

A theory of passive market impact ArXiv ID: 2412.07461 “View on arXiv” Authors: Unknown Abstract While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by developing a microstructure model connecting liquidity dynamics and price moves. A key innovation of our approach is to replace the traditional assumption of constant information content for each trade by a function that depends on the available volume in the limit order book. Within this framework, we explore scaling limits and analyze the market impact of passive metaorders. Additionally, we derive useful approximations for the shape of market impact curves, leading to closed-form formulas that can be easily applied in practice. ...

MarketGPT: Developing a Pre-trained transformer (GPT) for Modeling Financial Time Series ArXiv ID: 2411.16585 “View on arXiv” Authors: Unknown Abstract This work presents a generative pre-trained transformer (GPT) designed for modeling financial time series. The GPT functions as an order generation engine within a discrete event simulator, enabling realistic replication of limit order book dynamics. Our model leverages recent advancements in large language models to produce long sequences of order messages in a steaming manner. Our results demonstrate that the model successfully reproduces key features of order flow data, even when the initial order flow prompt is no longer present within the model’s context window. Moreover, evaluations reveal that the model captures several statistical properties, or ‘stylized facts’, characteristic of real financial markets and broader macro-scale data distributions. Collectively, this work marks a significant step toward creating high-fidelity, interactive market simulations. ...

How Wash Traders Exploit Market Conditions in Cryptocurrency Markets ArXiv ID: 2411.08720 “View on arXiv” Authors: Unknown Abstract Wash trading, the practice of simultaneously placing buy and sell orders for the same asset to inflate trading volume, has been prevalent in cryptocurrency markets. This paper investigates whether wash traders in Bitcoin act deliberately to exploit market conditions and identifies the characteristics of such manipulative behavior. Using a unique dataset of 18 million transactions from Mt. Gox, once the largest Bitcoin exchange, I find that wash trading intensifies when legitimate trading volume is low and diminishes when it is high, indicating strategic timing to maximize impact in less liquid markets. The activity also exhibits spillover effects across platforms and decreases when trading volumes in other asset classes like stocks or gold rise, suggesting sensitivity to broader market dynamics. Additionally, wash traders exploit periods of heightened media attention and online rumors to amplify their influence, causing rapid but short-lived spikes in legitimate trading volume. Using an exogenous demand shock associated with illicit online marketplaces, I find that wash trading responds to contemporaneous events affecting Bitcoin demand. These results advance the understanding of manipulative practices in digital currency markets and have significant implications for regulators aiming to detect and prevent wash trading. ...

Market efficiency, informational asymmetry and pseudo-collusion of adaptively learning agents ArXiv ID: 2411.05032 “View on arXiv” Authors: Unknown Abstract We examine the dynamics of informational efficiency in a market with asymmetrically informed, boundedly rational traders who adaptively learn optimal strategies using simple multiarmed bandit (MAB) algorithms. The strategies available to the traders have two dimensions: on the one hand, the traders must endogenously choose whether to acquire a costly information signal, on the other, they must determine how aggressively they trade by choosing the share of their wealth to be invested in the risky asset. Our study contributes to two strands of literature: the literature comparing the effects of competitive and strategic behavior on asset price efficiency under costly information as well as the actively growing literature on algorithmic tacit collusion and pseudo-collusion in financial markets. We find that for certain market environments (with low information costs) our model reproduces the results of Kyle [“1989”] in that the ability of traders to trade strategically leads to worse price efficiency compared to the purely competitive case. For other environments (with high information costs), on the other hand, our results show that a market with strategically acting traders can be more efficient than a purely competitive one. Furthermore, we obtain novel results on the ability of independently learning traders to coordinate on a pseudo-collusive behavior, leading to non-competitive pricing. Contrary to some recent contributions (see e.g. [“Cartea et al. 2022”]), we find that the pseudo-collusive behavior in our model is robust to a large number of agents, demonstrating that even in the setting of financial markets with a large number of independently learning traders non-competitive pricing and pseudo-collusive behavior can frequently arise. ...