Financial markets are complex systems characterized by high statistical noise, nonlinearity, and constant evolution. Thus, modeling them is extremely hard. We address the task of generating realistic and responsive Limit Order Book (LOB) market simulations, which are fundamental for calibrating and testing trading strategies, performing market impact experiments, and generating synthetic market data. Previous works lack realism, usefulness, and responsiveness of the generated simulations. To bridge this gap, we propose a novel TRAnsformer-based Denoising Diffusion Probabilistic Engine for LOB Simulations (TRADES). TRADES generates realistic order flows conditioned on the state of the market, leveraging a transformer-based architecture that captures the temporal and spatial characteristics of high-frequency market data. There is a notable absence of quantitative metrics for evaluating generative market simulation models in the literature. To tackle this problem, we adapt the predictive score, a metric measured as an MAE, by training a stock price predictive model on synthetic data and testing it on real data. We compare TRADES with previous works on two stocks, reporting an x3.27 and x3.47 improvement over SoTA according to the predictive score, demonstrating that we generate useful synthetic market data for financial downstream tasks. We assess TRADES's market simulation realism and responsiveness, showing that it effectively learns the conditional data distribution and successfully reacts to an experimental agent, giving sprout to possible calibrations and evaluations of trading strategies and market impact experiments. We developed DeepMarket, the first open-source Python framework for market simulation with deep learning. Our repository includes a synthetic LOB dataset composed of TRADES's generates simulations. We release the code at github.com/LeonardoBerti00/DeepMarket.

Traditional economic models often rely on fixed assumptions about market dynamics, limiting their ability to capture the complexities and stochastic nature of real-world scenarios. However, reality is more complex and includes noise, making traditional models assumptions not met in the market. In this paper, we explore the application of deep reinforcement learning (DRL) to obtain optimal production strategies in microeconomic market environments to overcome the limitations of traditional models. Concretely, we propose a DRL-based approach to obtain an effective policy in competitive markets with multiple producers, each optimizing their production decisions in response to fluctuating demand, supply, prices, subsidies, fixed costs, total production curve, elasticities and other effects contaminated by noise. Our framework enables agents to learn adaptive production policies to several simulations that consistently outperform static and random strategies. As the deep neural networks used by the agents are universal approximators of functions, DRL algorithms can represent in the network complex patterns of data learnt by trial and error that explain the market. Through extensive simulations, we demonstrate how DRL can capture the intricate interplay between production costs, market prices, and competitor behavior, providing insights into optimal decision-making in dynamic economic settings. The results show that agents trained with DRL can strategically adjust production levels to maximize long-term profitability, even in the face of volatile market conditions. We believe that the study bridges the gap between theoretical economic modeling and practical market simulation, illustrating the potential of DRL to revolutionize decision-making in market strategies.

Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite efforts to build real-world simulators, leveraging generative models for virtual worlds, like financial markets, remains underexplored. In financial markets, generative models can simulate market effects of various behaviors, enabling interaction with market scenes and players, 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 need for realistic, interactive and controllable order generation. Key objectives of this paper include evaluating LMM's scaling law in financial markets, assessing MarS's realism, balancing controlled generation with market impact, and demonstrating MarS's potential applications. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment. Our contributions include pioneering a generative model for financial markets, designing MarS to meet domain-specific needs, and demonstrating MarS-based applications' industry potential.

In this paper, we introduce DeepTraderX (DTX), a simple Deep Learning-based trader, and present results that demonstrate its performance in a multi-threaded market simulation. In a total of about 500 simulated market days, DTX has learned solely by watching the prices that other strategies produce. By doing this, it has successfully created a mapping from market data to quotes, either bid or ask orders, to place for an asset. Trained on historical Level-2 market data, i.e., the Limit Order Book (LOB) for specific tradable assets, DTX processes the market state $S$ at each timestep $T$ to determine a price $P$ for market orders. The market data used in both training and testing was generated from unique market schedules based on real historic stock market data. DTX was tested extensively against the best strategies in the literature, with its results validated by statistical analysis. Our findings underscore DTX's capability to rival, and in many instances, surpass, the performance of public-domain traders, including those that outclass human traders, emphasising the efficiency of simple models, as this is required to succeed in intricate multi-threaded simulations. This highlights the potential of leveraging "black-box" Deep Learning systems to create more efficient financial markets.

The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in macroeconomic outlook. In recent years, agent-based models have been developed that reproduce many features of an exchange, as summarised by a set of stylised facts and statistics. However, the ability to calibrate simulators to a specific period of trading remains an open challenge. In this work, we develop a novel approach to the calibration of market simulators by leveraging recent advances in deep learning, specifically using neural density estimators and embedding networks. We demonstrate that our approach is able to correctly identify high probability parameter sets, both when applied to synthetic and historical data, and without reliance on manually selected or weighted ensembles of stylised facts.

In many applications involving multi-agent system (MAS), it is imperative to test an experimental (Exp) autonomous agent in a high-fidelity simulator prior to its deployment to production, to avoid unexpected losses in the real-world. Such a simulator acts as the environmental background (BG) agent(s), called agent-based simulator (ABS), aiming to replicate the complex real MAS. However, developing realistic ABS remains challenging, mainly due to the sequential and dynamic nature of such systems. To fill this gap, we propose a metric to distinguish between real and synthetic multi-agent systems, which is evaluated through the live interaction between the Exp and BG agents to explicitly account for the systems' sequential nature. Specifically, we characterize the system/environment by studying the effect of a sequence of BG agents' responses to the environment state evolution and take such effects' differences as MAS distance metric; The effect estimation is cast as a causal inference problem since the environment evolution is confounded with the previous environment state. Importantly, we propose the Interactive Agent-Guided Simulation (INTAGS) framework to build a realistic ABS by optimizing over this novel metric. To adapt to any environment with interactive sequential decision making agents, INTAGS formulates the simulator as a stochastic policy in reinforcement learning. Moreover, INTAGS utilizes the policy gradient update to bypass differentiating the proposed metric such that it can support non-differentiable operations of multi-agent environments. Through extensive experiments, we demonstrate the effectiveness of INTAGS on an equity stock market simulation example. We show that using INTAGS to calibrate the simulator can generate more realistic market data compared to the state-of-the-art conditional Wasserstein Generative Adversarial Network approach.

This paper presents a new artificial market simulation platform, PAMS: Platform for Artificial Market Simulations. PAMS is developed as a Python-based simulator that is easily integrated with deep learning and enabling various simulation that requires easy users' modification. In this paper, we demonstrate PAMS effectiveness through a study using agents predicting future prices by deep learning.

Abstract: In a continuous-time setting we investigate how the management of a firm controls a dynamic choice between two generic voluntary disclosure decision rules (strategies): one a full and transparent disclosure referred to as candid, the other, referred to as sparing, under which items only above a dynamic threshold value are disclosed. We show how management are rewarded with a reputational premium for being candid. The candid strategy is, however, costly because the alternative of sparing behaviour shields from a downgrade in disclosed low values. We show how parameters of the model such as news intensity, pay-for-performance and time-to-mandatory-disclosure determine the optimal choice of candid versus sparing strategies and optimal times for management to switch between the two. The private news updates received by management are modelled following a Poisson arrival process, occurring between the fixed (known) mandatory disclosure dates, such as fiscal years or quarters, with the news received by management generated by a background Black-Scholes model of economic activity and of its partial observation.

Multi-agent market simulation is an effective tool to investigate the impact of various trading strategies in financial markets. One way of designing a trading agent in simulated markets is through reinforcement learning where the agent is trained to optimize its cumulative rewards (e.g., maximizing profits, minimizing risk, improving equitability). While the agent learns a rational policy that optimizes the reward function, in reality, human investors are sub-rational with their decisions often differing from the optimal. In this work, we model human sub-rationality as resulting from two possible causes: psychological bias and computational limitation. We first examine the relationship between investor profits and their degree of sub-rationality, and create hand-crafted market scenarios to intuitively explain the sub-rational human behaviors. Through experiments, we show that our models successfully capture human sub-rationality as observed in the behavioral finance literature. We also examine the impact of sub-rational human investors on market observables such as traded volumes, spread and volatility. We believe our work will benefit research in behavioral finance and provide a better understanding of human trading behavior.