Market Microstructure

Double Auctions: Formalization and Automated Checkers ArXiv ID: 2410.18751 “View on arXiv” Authors: Unknown Abstract Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how these requests are to be matched. The two most common objectives for determining the matching are maximizing trade volume at a uniform price and maximizing trade volume through dynamic pricing. Prior research has primarily focused on single-quantity trade requests. In this work, we extend the framework to handle multiple-quantity trade requests and present fully formalized matching algorithms for double auctions, along with their correctness proofs. We establish new uniqueness theorems, enabling automatic detection of violations in exchange systems by comparing their output to that of a verified program. All proofs are formalized in the Coq Proof Assistant, and we extract verified OCaml and Haskell programs that could serve as a resource for exchanges and market regulators. We demonstrate the practical applicability of our work by running the verified program on real market data from an exchange to automatically check for violations in the exchange algorithm. ...

No Tick-Size Too Small: A General Method for Modelling Small Tick Limit Order Books ArXiv ID: 2410.08744 “View on arXiv” Authors: Unknown Abstract Tick-sizes not only influence the granularity of the price formation process but also affect market agents’ behavior. We investigate the disparity in the microstructural properties of the Limit Order Book (LOB) across a basket of assets with different relative tick-sizes. A key contribution of this study is the identification of several stylized facts, which are used to differentiate between large, medium, and small-tick assets, along with clear metrics for their measurement. We provide cross-asset visualizations to illustrate how these attributes vary with relative tick-size. Further, we propose a Hawkes Process model that {"\color{black"}not only fits well for large-tick assets, but also accounts for }sparsity, multi-tick level price moves, and the shape of the LOB in small-tick assets. Through simulation studies, we demonstrate the {"\color{black"} versatility} of the model and identify key variables that determine whether a simulated LOB resembles a large-tick or small-tick asset. Our tests show that stylized facts like sparsity, shape, and relative returns distribution can be smoothly transitioned from a large-tick to a small-tick asset using our model. We test this model’s assumptions, showcase its challenges and propose questions for further directions in this area of research. ...

Simulating and analyzing a sparse order book: an application to intraday electricity markets ArXiv ID: 2410.06839 “View on arXiv” Authors: Unknown Abstract This paper presents a novel model for simulating and analyzing sparse limit order books (LOBs), with a specific application to the European intraday electricity market. In illiquid markets, characterized by significant gaps between order levels due to sparse trading volumes, traditional LOB models often fall short. Our approach utilizes an inhomogeneous Poisson process to accurately capture the sporadic nature of order arrivals and cancellations on both the bid and ask sides of the book. By applying this model to the intraday electricity market, we gain insights into the unique microstructural behaviors and challenges of this dynamic trading environment. The results offer valuable implications for market participants, enhancing their understanding of LOB dynamics in illiquid markets. This work contributes to the broader field of market microstructure by providing a robust framework adaptable to various illiquid market settings beyond electricity trading. ...

A Comparison between Financial and Gambling Markets ArXiv ID: 2409.13528 “View on arXiv” Authors: Unknown Abstract Financial and gambling markets are ostensibly similar and hence strategies from one could potentially be applied to the other. Financial markets have been extensively studied, resulting in numerous theorems and models, while gambling markets have received comparatively less attention and remain relatively undocumented. This study conducts a comprehensive comparison of both markets, focusing on trading rather than regulation. Five key aspects are examined: platform, product, procedure, participant and strategy. The findings reveal numerous similarities between these two markets. Financial exchanges resemble online betting platforms, such as Betfair, and some financial products, including stocks and options, share speculative traits with sports betting. We examine whether well-established models and strategies from financial markets could be applied to the gambling industry, which lacks comparable frameworks. For example, statistical arbitrage from financial markets has been effectively applied to gambling markets, particularly in peer-to-peer betting exchanges, where bettors exploit odds discrepancies for risk-free profits using quantitative models. Therefore, exploring the strategies and approaches used in both markets could lead to new opportunities for innovation and optimization in trading and betting activities. ...

Bellwether Trades: Characteristics of Trades influential in Predicting Future Price Movements in Markets ArXiv ID: 2409.05192 “View on arXiv” Authors: Unknown Abstract In this study, we leverage powerful non-linear machine learning methods to identify the characteristics of trades that contain valuable information. First, we demonstrate the effectiveness of our optimized neural network predictor in accurately predicting future market movements. Then, we utilize the information from this successful neural network predictor to pinpoint the individual trades within each data point (trading window) that had the most impact on the optimized neural network’s prediction of future price movements. This approach helps us uncover important insights about the heterogeneity in information content provided by trades of different sizes, venues, trading contexts, and over time. ...

MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model ArXiv ID: 2409.07486 “View on arXiv” Authors: Unknown Abstract Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite significant efforts to build real-world simulators, the application of generative models to virtual worlds, like financial markets, remains under-explored. In financial markets, generative models can simulate complex market effects of participants with various behaviors, enabling interaction under different market conditions, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the domain-specific need for realistic, interactive and controllable order generation. Key observations include LMM’s strong scalability across data size and model complexity, and MarS’s robust and practicable realism in controlled generation with market impact. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment, thus demonstrating MarS’s “paradigm shift” potential for a variety of financial applications. We release the code of MarS at https://github.com/microsoft/MarS/. ...

Attention-Based Reading, Highlighting, and Forecasting of the Limit Order Book ArXiv ID: 2409.02277 “View on arXiv” Authors: Unknown Abstract Managing high-frequency data in a limit order book (LOB) is a complex task that often exceeds the capabilities of conventional time-series forecasting models. Accurately predicting the entire multi-level LOB, beyond just the mid-price, is essential for understanding high-frequency market dynamics. However, this task is challenging due to the complex interdependencies among compound attributes within each dimension, such as order types, features, and levels. In this study, we explore advanced multidimensional sequence-to-sequence models to forecast the entire multi-level LOB, including order prices and volumes. Our main contribution is the development of a compound multivariate embedding method designed to capture the complex relationships between spatiotemporal features. Empirical results show that our method outperforms other multivariate forecasting methods, achieving the lowest forecasting error while preserving the ordinal structure of the LOB. ...

Correlation emergence in two coupled simulated limit order books ArXiv ID: 2408.03181 “View on arXiv” Authors: Unknown Abstract We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the mean-reversion between the two order books in the fluid limit for a Lit order book with vanishing boundary conditions and order volume conservation. We are able to demonstrate the recovery of an Epps effect from this. We discuss how various stylised facts depend on the model parameters and the numerical scheme and discuss the various strengths and weaknesses of the approach. We demonstrate how the Epps effect depends on different choices of time and price discretisation. This shows how an Epps effect can emerge without recourse to market microstructure noise relative to a latent model but can rather be viewed as an emergent property arising from trader interactions in a world of asynchronous events. ...

Lower Bounds of Uncertainty of Observations of Macroeconomic Variables and Upper Limits on the Accuracy of Their Forecasts ArXiv ID: 2408.04644 “View on arXiv” Authors: Unknown Abstract This paper defines theoretical lower bounds of uncertainty of observations of macroeconomic variables that depend on statistical moments and correlations of random values and volumes of market trades. Any econometric assessments of macroeconomic variables have greater uncertainty. We consider macroeconomic variables as random that depend on random values and volumes of trades. To predict random macroeconomic variables, one should forecast their probabilities. Upper limits on the accuracy of the forecasts of probabilities of macroeconomic variables, prices, and returns depend on the number of predicted statistical moments. We consider economic obstacles that limit by the first two the number of predicted statistical moments. The accuracy of any forecasts of probabilities of random macroeconomic variables, prices, returns, and market trades doesn’t exceed the accuracy of Gaussian approximations. Any forecasts of macroeconomic variables have uncertainty higher than one determined by predictions of coefficients of variation of random values and volumes of trades. ...

Nash Equilibrium between Brokers and Traders ArXiv ID: 2407.10561 “View on arXiv” Authors: Unknown Abstract We study the perfect information Nash equilibrium between a broker and her clients – an informed trader and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with the broker. The informed trader and the broker maximise expected wealth subject to inventory penalties, while the uninformed trader is not strategic and sends the broker random buy and sell orders. We characterise the Nash equilibrium of the trading strategies with the solution to a coupled system of forward-backward stochastic differential equations (FBSDEs). We solve this system explicitly and study the effect of information, profitability, and inventory control in the trading strategies of the broker and the informed trader. ...