Market Impact

Position building in competition is a game with incomplete information ArXiv ID: 2501.01241 “View on arXiv” Authors: Unknown Abstract This paper examines strategic trading under incomplete information, where firms lack full knowledge of key aspects of their competitors’ trading strategies such as target sizes and market impact models. We extend previous work on competitive trading equilibria by incorporating uncertainty through the framework of Bayesian games. This allows us to analyze scenarios where firms have diverse beliefs about market conditions and each other’s strategies. We derive optimal trading strategies in this setting and demonstrate how uncertainty significantly impacts these strategies compared to the complete information case. Furthermore, we introduce a novel approach to model the presence of non-strategic traders, even when strategic firms disagree on their characteristics. Our analysis reveals the complex interplay of beliefs and strategic adjustments required in such an environment. Finally, we discuss limitations of the current model, including the reliance on linear market impact and the lack of dynamic strategy adjustments, outlining directions for future research. ...

Optimal Execution Strategies Incorporating Internal Liquidity Through Market Making ArXiv ID: 2501.07581 “View on arXiv” Authors: Unknown Abstract This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{“cartea2015algorithmic”} framework, we incorporate market impact in interbank orders while excluding it for internal market-making transactions. Our model aims to optimize the balance between interbank and internal liquidity, reducing market impact and improving execution efficiency. ...

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. ...

Volatility-Volume Order Slicing via Statistical Analysis ArXiv ID: 2412.12482 “View on arXiv” Authors: Unknown Abstract This paper addresses the challenges faced in large-volume trading, where executing substantial orders can result in significant market impact and slippage. To mitigate these effects, this study proposes a volatility-volume-based order slicing strategy that leverages Exponential Weighted Moving Average and Markov Chain Monte Carlo simulations. These methods are used to dynamically estimate future trading volumes and price ranges, enabling traders to adapt their strategies by segmenting order execution sizes based on these predictions. Results show that the proposed approach improves trade execution efficiency, reduces market impact, and offers a more adaptive solution for volatile market conditions. The findings have practical implications for large-volume trading, providing a foundation for further research into adaptive execution strategies. ...

Uncertain Regulations, Definite Impacts: The Impact of the US Securities and Exchange Commission’s Regulatory Interventions on Crypto Assets ArXiv ID: 2412.02452 “View on arXiv” Authors: Unknown Abstract This study employs an event study methodology to investigate the market impact of the U.S. Securities and Exchange Commission’s (SEC) classification of crypto assets as securities. It explores how SEC interventions influence asset returns and trading volumes, focusing on explicitly named crypto assets. The empirical analysis highlights significant adverse market reactions, notably returns plummeting 12% over one week post-announcement, persisting for a month. We demonstrate that the severity of market reaction depends on sentiment and asset characteristics such as market size, age, volatility, and illiquidity. Further, we identify significant ex-ante trading volume effects indicative of pre-announcement informed trading. ...

Optimal execution with deterministically time varying liquidity: well posedness and price manipulation ArXiv ID: 2410.04867 “View on arXiv” Authors: Unknown Abstract We investigate the well-posedness in the Hadamard sense and the absence of price manipulation in the optimal execution problem within the Almgren-Chriss framework, where the temporary and permanent impact parameters vary deterministically over time. We present sufficient conditions for the existence of a unique solution and provide second-order conditions for the problem, with a particular focus on scenarios where impact parameters change monotonically over time. Additionally, we establish conditions to prevent transaction-triggered price manipulation in the optimal solution, i.e. the occurence of buying and selling in the same trading program. Our findings are supported by numerical analyses that explore various regimes in simple parametric settings for the dynamics of impact parameters. ...

Limit Order Book Simulation and Trade Evaluation with $K$-Nearest-Neighbor Resampling ArXiv ID: 2409.06514 “View on arXiv” Authors: Unknown Abstract In this paper, we show how $K$-nearest neighbor ($K$-NN) resampling, an off-policy evaluation method proposed in \cite{“giegrich2023k”}, can be applied to simulate limit order book (LOB) markets and how it can be used to evaluate and calibrate trading strategies. Using historical LOB data, we demonstrate that our simulation method is capable of recreating realistic LOB dynamics and that synthetic trading within the simulation leads to a market impact in line with the corresponding literature. Compared to other statistical LOB simulation methods, our algorithm has theoretical convergence guarantees under general conditions, does not require optimization, is easy to implement and computationally efficient. Furthermore, we show that in a benchmark comparison our method outperforms a deep learning-based algorithm for several key statistics. In the context of a LOB with pro-rata type matching, we demonstrate how our algorithm can calibrate the size of limit orders for a liquidation strategy. Finally, we describe how $K$-NN resampling can be modified for choices of higher dimensional state spaces. ...

Optimal position-building strategies in competition ArXiv ID: 2409.03586 “View on arXiv” Authors: Unknown Abstract This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in the space of trading strategies where action sets are trading strategies and traders try to devise best-response strategies to their adversaries. In this setup trading is guided by a desire to minimize the total cost of trading arising from a mixture of temporary and permanent market impact caused by the aggregate level of trading including the trader and the competition. We describe a notion of equilibrium strategies, show that they exist and provide closed-form solutions. ...

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/. ...

Deviations from the Nash equilibrium and emergence of tacit collusion in a two-player optimal execution game with reinforcement learning ArXiv ID: 2408.11773 “View on arXiv” Authors: Unknown Abstract The use of reinforcement learning algorithms in financial trading is becoming increasingly prevalent. However, the autonomous nature of these algorithms can lead to unexpected outcomes that deviate from traditional game-theoretical predictions and may even destabilize markets. In this study, we examine a scenario in which two autonomous agents, modeled with Double Deep Q-Learning, learn to liquidate the same asset optimally in the presence of market impact, using the Almgren-Chriss (2000) framework. Our results show that the strategies learned by the agents deviate significantly from the Nash equilibrium of the corresponding market impact game. Notably, the learned strategies exhibit tacit collusion, closely aligning with the Pareto-optimal solution. We further explore how different levels of market volatility influence the agents’ performance and the equilibria they discover, including scenarios where volatility differs between the training and testing phases. ...