Limit Order Book

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. ...

Market Simulation under Adverse Selection ArXiv ID: 2409.12721 “View on arXiv” Authors: Unknown Abstract In this paper, we study the effects of fill probabilities and adverse fills on the trading strategy simulation process. We specifically focus on a stochastic optimal control market-making problem and test the strategy on ES (E-mini S&P 500), NQ (E-mini Nasdaq 100), CL (Crude Oil) and ZN (10-Year Treasury Note), which are some of the most liquid futures contracts listed on the CME (Chicago Mercantile Exchange). We provide empirical evidence that shows how fill probabilities and adverse fills can significantly affect performance and propose a more prudent simulation framework to deal with this. Many previous works aim to measure different types of adverse selection in the limit order book (LOB), however, they often simulate price processes and market orders independently. This has the ability to largely inflate the performance of a short-term style trading strategy. Our studies show that using more realistic fill probabilities and tracking adverse fills in the strategy simulation process more accurately shows how these types of trading strategies would perform in reality. ...

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/. ...

Consistent time travel for realistic interactions with historical data: reinforcement learning for market making ArXiv ID: 2408.02322 “View on arXiv” Authors: Unknown Abstract Reinforcement learning works best when the impact of the agent’s actions on its environment can be perfectly simulated or fully appraised from available data. Some systems are however both hard to simulate and very sensitive to small perturbations. An additional difficulty arises when a RL agent is trained offline to be part of a multi-agent system using only anonymous data, which makes it impossible to infer the state of each agent, thus to use data directly. Typical examples are competitive systems without agent-resolved data such as financial markets. We introduce consistent data time travel for offline RL as a remedy for these problems: instead of using historical data in a sequential way, we argue that one needs to perform time travel in historical data, i.e., to adjust the time index so that both the past state and the influence of the RL agent’s action on the system coincide with real data. This both alleviates the need to resort to imperfect models and consistently accounts for both the immediate and long-term reactions of the system when using anonymous historical data. We apply this idea to market making in limit order books, a notoriously difficult task for RL; it turns out that the gain of the agent is significantly higher with data time travel than with naive sequential data, which suggests that the difficulty of this task for RL may have been overestimated. ...

The Negative Drift of a Limit Order Fill ArXiv ID: 2407.16527 “View on arXiv” Authors: Unknown Abstract Market making refers to a form of trading in financial markets characterized by passive orders which add liquidity to limit order books. Market makers are important for the proper functioning of financial markets worldwide. Given the importance, financial mathematics has endeavored to derive optimal strategies for placing limit orders in this context. This paper identifies a key discrepancy between popular model assumptions and the realities of real markets, specifically regarding the dynamics around limit order fills. Traditionally, market making models rely on an assumption of low-cost random fills, when in reality we observe a high-cost non-random fill behavior. Namely, limit order fills are caused by and coincide with adverse price movements, which create a drag on the market maker’s profit and loss. We refer to this phenomenon as “the negative drift” associated with limit order fills. We describe a discrete market model and prove theoretically that the negative drift exists. We also provide a detailed empirical simulation using one of the most traded financial instruments in the world, the 10 Year US Treasury Bond futures, which also confirms its existence. To our knowledge, this is the first paper to describe and prove this phenomenon in such detail. ...

HLOB – Information Persistence and Structure in Limit Order Books ArXiv ID: 2405.18938 “View on arXiv” Authors: Unknown Abstract We introduce a novel large-scale deep learning model for Limit Order Book mid-price changes forecasting, and we name it `HLOB’. This architecture (i) exploits the information encoded by an Information Filtering Network, namely the Triangulated Maximally Filtered Graph, to unveil deeper and non-trivial dependency structures among volume levels; and (ii) guarantees deterministic design choices to handle the complexity of the underlying system by drawing inspiration from the groundbreaking class of Homological Convolutional Neural Networks. We test our model against 9 state-of-the-art deep learning alternatives on 3 real-world Limit Order Book datasets, each including 15 stocks traded on the NASDAQ exchange, and we systematically characterize the scenarios where HLOB outperforms state-of-the-art architectures. Our approach sheds new light on the spatial distribution of information in Limit Order Books and on its degradation over increasing prediction horizons, narrowing the gap between microstructural modeling and deep learning-based forecasting in high-frequency financial markets. ...

Clearing time randomization and transaction fees for auction market design ArXiv ID: 2405.09764 “View on arXiv” Authors: Unknown Abstract Flaws of a continuous limit order book mechanism raise the question of whether a continuous trading session and a periodic auction session would bring better efficiency. This paper wants to go further in designing a periodic auction when both a continuous market and a periodic auction market are available to traders. In a periodic auction, we discover that a strategic trader could take advantage of the accumulated information available along the auction duration by arriving at the latest moment before the auction closes, increasing the price impact on the market. Such price impact moves the clearing price away from the efficient price and may disturb the efficiency of a periodic auction market. We thus propose and quantify the effect of two remedies to mitigate these flaws: randomizing the auction’s closing time and optimally designing a transaction fees policy for both the strategic traders and other market participants. Our results show that these policies encourage a strategic trader to send their orders earlier to enhance the efficiency of the auction market, illustrated by data extracted from Alphabet and Apple stocks. ...

Deep Limit Order Book Forecasting ArXiv ID: 2403.09267 “View on arXiv” Authors: Unknown Abstract We exploit cutting-edge deep learning methodologies to explore the predictability of high-frequency Limit Order Book mid-price changes for a heterogeneous set of stocks traded on the NASDAQ exchange. In so doing, we release `LOBFrame’, an open-source code base to efficiently process large-scale Limit Order Book data and quantitatively assess state-of-the-art deep learning models’ forecasting capabilities. Our results are twofold. We demonstrate that the stocks’ microstructural characteristics influence the efficacy of deep learning methods and that their high forecasting power does not necessarily correspond to actionable trading signals. We argue that traditional machine learning metrics fail to adequately assess the quality of forecasts in the Limit Order Book context. As an alternative, we propose an innovative operational framework that evaluates predictions’ practicality by focusing on the probability of accurately forecasting complete transactions. This work offers academics and practitioners an avenue to make informed and robust decisions on the application of deep learning techniques, their scope and limitations, effectively exploiting emergent statistical properties of the Limit Order Book. ...

Fill Probabilities in a Limit Order Book with State-Dependent Stochastic Order Flows ArXiv ID: 2403.02572 “View on arXiv” Authors: Unknown Abstract This paper focuses on computing the fill probabilities for limit orders positioned at various price levels within the limit order book, which play a crucial role in optimizing executions. We adopt a generic stochastic model to capture the dynamics of the order book as a series of queueing systems. This generic model is state-dependent and also incorporates stylized factors. We subsequently derive semi-analytical expressions to compute the relevant probabilities within the context of state-dependent stochastic order flows. These probabilities cover various scenarios, including the probability of a change in the mid-price, the fill probabilities of orders posted at the best quotes, and those posted at a price level deeper than the best quotes in the book, before the opposite best quote moves. These expressions can be further generalized to accommodate orders posted even deeper in the order book, although the associated probabilities are typically very small in such cases. Lastly, we conduct extensive numerical experiments using real order book data from the foreign exchange spot market. Our findings suggest that the model is tractable and possesses the capability to effectively capture the dynamics of the limit order book. Moreover, the derived formulas and numerical methods demonstrate reasonably good accuracy in estimating the fill probabilities. ...

Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes ArXiv ID: 2402.04740 “View on arXiv” Authors: Unknown Abstract An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive literature has been dedicated to the non-parametric estimation of both the linear and non-linear Hawkes process, there remains a significant gap in the literature regarding the marked Hawkes process. In response to this, we propose a methodology for estimating the conditional intensity of the marked Hawkes process. We introduce two distinct models: \textit{“Shallow Neural Hawkes with marks”}- for Hawkes processes with excitatory kernels and \textit{“Neural Network for Non-Linear Hawkes with Marks”}- for non-linear Hawkes processes. Both these approaches take the past arrival times and their corresponding marks as the input to obtain the arrival intensity. This approach is entirely non-parametric, preserving the interpretability associated with the marked Hawkes process. To validate the efficacy of our method, we subject the method to synthetic datasets with known ground truth. Additionally, we apply our method to model cryptocurrency order book data, demonstrating its applicability to real-world scenarios. ...