MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model

## Abstract

Abstract 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.

## 1 Introduction

The primary aim of generative models is to simulate realistic effects of various actions across different contexts, such as text generation (Achiam et al., ) and visual effects (Brooks et al., ). Real-world simulators enable human interaction with diverse scenes and objects (Mialon et al., ), allow robots to learn from simulated experiences without physical risk (Du et al., ), and generate vast amounts of realistic data for training other machine intelligence (Li et al., ).

Research on real-world simulators is extensive (Zhu et al., ; Yang et al., ), but the application of generative models for virtual world simulation remains underexplored. The financial market exemplifies such a virtual world. Here, generative models aim to simulate market effects of various financial behaviors. This allows human interaction with diverse scenarios, enables trading strategies to learn without financial risk, and generates vast data for other machine intelligence in finance.

The foundation of this simulation is domain-specific structured data, including orders, order batches, and the Limit Order Book (LOB) (Gould et al., ). In financial markets, certain information, such as gaming behaviors, transactional trends, and high-resolution market dynamics, is better captured through trading orders and batches rather than text. We propose that the generation of orders, order batches, and LOBs will play a role in financial markets similar to that of language modeling in the digital world. We term our generative market model the Large Market Model (LMM), aiming to replicate the success of recent large language models.

In this paper, we introduce a financial Market Simulation engine (MarS) powered by LMM, addressing the domain-specific requirement of modelling orders’ market impact and controllable generation with high realistic. The key objectives are: (1) Scaling Law Evaluation: Assessing LMM’s scalability in financial markets to demonstrate its potential. (2) Realism Assessment: Determining if MarS simulations are realistic enough for financial downstream tasks, indicating practical applicability. (3) Controlled Generation and Market Impact: Evaluating the trade-off between controlled generation and market impact from injected orders, highlighting our domain-specific design. (4) Downstream Applications: Showcasing potential capabilities of applications built on MarS.

For years, researchers in the finance sector have actively embraced AI techniques. Once a new AI algorithm or model has been proven effective in traditional AI scenarios, finance researchers adapt and apply these techniques to financial contexts, designing specific models and algorithms for individual scenarios and tasks(Zhang et al., ; Liu et al., ; Kim et al., ; Hou et al., ). However, few AI techniques have originally emerged from financial scenarios and the unique data within finance. Our MarS is the first to purely leverage fundamental elements of the financial market and specially designed AI technology, serving as a unified interface for various financial downstream tasks. We posit that MarS has the potential to bring paradigm shifts to a wide range of tasks related to the financial market.
While MarS’s potential downstream applications are broad, we demonstrate four key use cases:

- 1.
Forecast Tool: MarS generates subsequent orders based on recent orders and the limit order book (LOB), simulating future market trajectories. This enables precise forecasting by analyzing multiple simulated trajectories.
- 2.
Detection System: By generating multiple future market trajectories, MarS identifies potential risks not apparent from current observations. For example, a sudden drop in trajectory variance could indicate an impending significant event, providing early warnings and enhancing risk management.
- 3.
Analysis Platform: MarS answers a wide range of “what if” questions by providing a realistic simulation environment. For instance, it evaluates the market impact of large orders by comparing existing market impact formulas to simulated results, identifying potential improvements and gaining deeper insights into market dynamics.
- 4.
Agent Training Environment: The realistic and responsive nature of MarS makes it ideal for training reinforcement learning agents. This is demonstrated with an order execution scenario, showcasing MarS’s potential for developing and refining trading strategies without real-world financial risks.

The main contributions of this paper are as follows:

- •
We take the first step toward building a generative foundation model as a world model for financial market and verify the scaling law of the Large Market Model. It demonstrates the huge potential of this new direction of domain-specific foundation models.
- •
We design a realistic Market Simulation based on the LMM to fulfill two key requirements: generating target scenarios and modeling order market impacts, thereby unlocking LMM’s potential for meaningful applications.
- •
We showcase four types of downstream applications of MarS, demonstrating the significant potential of the MarS-based paradigm for the industry.

Figure: Figure 1: High-Level Overview of MarS.MarS is powered by a generative foundation model (LMM) trained on order-level historical financial market data. During real-time simulation, LMM dynamically generates order series in response to various conditions, including user-submitted interactive orders, vague target scenario descriptions, and current/recent market data. These generated order series, combined with user interactive orders, are matched in a simulated clearing house in real-time, producing fine-grained simulated market trajectories. The flexibility of LMM’s order generation enables MarS to support various downstream applications, such as forecasting, detection/warning systems, analysis platforms, and agent training environments.
Refer to caption: x1.png

## 2 MarS Design

To achieve a truly Realistic simulation system, MarS must excel in three key dimensions: high-resolution, controllability, and interactivity.

High-resolution refers to the ability of MarS to faithfully replicate the intricate dynamics of financial markets. This is why we leverage trading orders and order batches as the foundational elements of our simulations. These orders, which encapsulate the investment behaviors of market participants, allow us to accurately reproduce historical market trajectories by matching them with corresponding order matching rules. This fine-grained approach is essential for creating simulations that are not just realistic but deeply reflective of actual market conditions.

Controllability in MarS is about offering the flexibility to simulate a wide range of market scenarios and circumstances. Whether studying market trends, monitoring potential risks, or optimizing trading strategies, MarS provides the tools needed to explore any possible market condition. This capability is particularly valuable for stress testing and strategy optimization, where diverse and even rare extreme cases must be modeled accurately.

Interactivity is another crucial aspect, enabling users to interact directly with the simulated market. This allows for the evaluation of market impacts, including first-order and second-order effects, which are critical for analyzing trading strategies, assessing systemic risks, managing risks effectively, and informing regulatory policies. By engaging with these interactive simulations, users can gain deeper insights into the potential outcomes of their actions in a controlled, risk-free environment.

### 2.1 Conditional Trading Order Generation

We denote an order clip as a sequence of trading orders $\mathbf{x}=(x_{0},\ldots,x_{n})$. Both controllable and interactive characteristics can be formed in the conditions of a conditional generation process of $\mathbf{x}$. In MarS, the full condition list contains four parts:

- 1.
DES_TEXT provides a vague description of the desired market scenario for $\mathbf{x}$ (e.g., “price bump” or “volatility crush”), fulfilling the controllable characteristic of MarS.
- 2.
$(\dot{x}_{i+1},\ldots,\dot{x}_{i+j})$ represents $j$ interactive orders injected by the user after the $i$-th generated order, forming the $i+1$ to $i+j$ orders in $\mathbf{x}$. If $j=0$, there is no interactive order between $x_{i}$ and $x_{i+1}$ in $\mathbf{x}$. This fulfills the interactive characteristic of MarS.
- 3.
$(x_{0},\ldots,x_{m})$ represents $m$ orders as the starting sequence of the target generated order sequence $\mathbf{x}$. A common scenario is using the most recent real orders as a condition to generate subsequent orders as a forecast. This enables simulation based on historical/recent real markets, crucial for practical applications of MarS.
- 4.
MTCH_R represents the matching rules of trading orders $\mathbf{x}$, which vary slightly between financial markets. It defines the feasible space of each order in $\mathbf{x}$ and indicates the specialty of the corresponding financial market (e.g., overall trading behavior of its participants). This ensures MarS provides a realistic simulation for a specified financial market.

Given the above conditions, the dynamic conditional order generation models the conditional probability $p(x_{i+j+1}|\{\textit{DES_TEXT},(\dot{x}_{i+1},\ldots,\dot{x}_{i+j}),(x_{0},
\ldots,x_{m}),\textit{MTCH_R}\})$ for each non-interactive order in $\mathbf{x}$. These conditions can be adjusted for various MarS scenarios. We will showcase several application types with different conditions in Sec. 4.

### 2.2 Large Market Model for Modelling the Financial Market

#### 2.2.1 Framework Design of Large Market Model

The Large Market Model (LMM) is designed with a robust architecture that integrates two complementary modeling approaches: Order Sequence Modeling and Order-Batch Sequence Modeling. These approaches are combined into an ensemble model to leverage their individual strengths while addressing the complexities of financial market simulations.

- •
Order Sequence Modeling. To accurately capture market dynamics and the impact of individual orders, we employ a causal transformer on the order sequence. Each order is encoded along with its preceding Limit Order Book (LOB) information as a single token using a custom design. This approach allows the model to reflect the sequential nature of market orders, ensuring that each order’s context within the broader market activity is preserved. The causal transformer enables the generation of order sequences that realistically mirror the flow and impact of trades within the market.
- •
Order-Batch Sequence Modeling. While order sequences capture the flow of individual trades, financial markets also exhibit structured patterns over aggregated time intervals, such as minutes or hours. To model these patterns, we apply an auto-regressive transformer to order-batch sequences. This approach aligns the control signals at each time step and adheres to realistic time series patterns. Orders within a specific time step are grouped into batches and converted into a structured representation that captures the overall market behavior during that period. A two-step tokenization and sequence modeling approach is then applied, ensuring that the generated order batches maintain coherence and continuity over time.
- •
Ensemble Model for Orders and Order Batches. The distinct advantages of order sequence modeling and order-batch sequence modeling necessitate their integration into a cohesive framework. The ensemble model we designed combines these two approaches, enabling improved market modeling and generation. It achieves this by balancing the fine-grained control of individual orders from the order model with the broader market dynamics captured by the order-batch model. This integration ensures that the generated market simulations are both detailed and contextually accurate, reflecting realistic market conditions.
- •
Fine-grained Signal Generation Interface. To enhance the controllability of MarS, we introduce a fine-grained signal generation interface. This interface can map vague descriptions in natural language or general configurations to fine-grained series of control signals. We provide an implementation that leverages LLM-based historical market record retrieval to generate precise control signals (e.g., price, volume) from vague descriptive prompts, such as DES_TEXT. These signals guide the ensemble model, ensuring that the simulations not only follow realistic market patterns but also adhere to specific user-defined scenarios. This capability is crucial for stress testing, strategy optimization, and scenario analysis, making MarS a versatile tool for financial market simulations.

The bottom-left of Fig.1 shows the framework of the Large Market Model. The detailed design of its four parts can be found in Appendix.

#### 2.2.2 Scaling Law in Large Market Model

In the design of our four-part foundation model, we employ both an auto-regressive transformer for the order-batch sequence and a causal transformer for the order sequence. These components utilize standard pre-training techniques commonly applied in foundation models, including those used in language modeling (Kaplan et al., ) and vision modeling (Zhai et al., ).

To assess the scalability of the Large Market Model (LMM), we evaluated its performance across varying data scales and model sizes. Our findings indicate that as the size of the data and the model increases, the performance of the LMM significantly improves, consistent with the scaling laws observed in other foundation models. This suggests that the potential of LMM can be further unlocked by leveraging larger datasets and more extensive computational resources.

While our current implementation only taps into a fraction of the available order-level financial market data due to resource constraints, the vast amount of data accessible within financial markets holds tremendous promise for future enhancements. MarS, in this context, serves as the tool to unearth this ”gold mine” of data, indicating substantial opportunities for more comprehensive and powerful market simulations.

Figure: Figure 2: Scaling curve of Order Model and Order-batch Model. Left: Order Model. Trained on 32 billion tokens. Model sizes: 2 million to 1.02 billion parameters. Right: Order-batch Model. Trained on 10 billion tokens. Model sizes: 150 million to 3 billion parameters. Results show superior performance with increased data and model sizes.
Refer to caption: x2.png

### 2.3 MarS — Order Generation Combined with Simulated Clearing House

After pre-training LMM, realistic order streams for market simulation can be generated. A simulated clearing house matches both generated and interactive orders, providing extensive information (e.g., limit order book) for subsequent order generation. This clearing house merges generated and interactive orders in real-time. For example, after generating order $x_{i}$, the clearing house waits for $j$ interactive orders ($j\geq 0$). The order match engine sequentially matches $x_{i}$ with the $j$ interactive orders, then sends the matching results back to LMM for generating the next order $x_{i+j+1}$.

The trade-off between market impact and control signal is crucial for realistic simulation and achieving the three characteristics of MarS. We adhere to two guiding principles to ensure a realistic trade-off, applying them in the order-batch generation process.

- •
“Shaping the Future Based on Realized Realities”. At each time step, order-batch model generates the next order-batch based on recent data from the simulated clearing house.
- •
“Electing the Best from Every Possible Future”. At each time step, multiple predicted order-batches are generated. The best match to the fine-grained control signal is selected, enabling soft control of order-batch generation.

The order-level transformer, trained on historical orders, naturally learns market impact for subsequent order generation. Concurrently, the ensemble model influences order generation, aligning with the generated next order-batch. Figure 3 illustrates the generation process, balancing market impact and control signals to form a realistic simulation.

Figure: Figure 3: The process of MarS generation. There is a two-level order generation in MarS — minute-level order-batch generation and individual order generation. Order-Batch Level: At the end of $\textit{minute}_{t}$, all generated and interactive orders are counted as the realized order-batch distribution and appended to a series. Following the ”Shaping the Future Based on Realized Realities” principle, the Order-batch model generates $N$ possible distributions for $\textit{minute}_{t+1}$ based on the series. Then, following the ”Electing the Best from Every Possible Future” principle, the target distribution ($\star$) is selected based on the consistency of the minute-level control signal. Order Level: The Order Model generates immediate responses for recent and user-submitted interactive orders. A logits vector indicates the expected distribution of the next order. To balance market impact and controlled generation, an ensemble model refines the next order distribution based on the target order-batch distribution of $\textit{minute}_{t+1}$ ($\star$). By sampling from refined logits, an order is generated in $\textit{minute}_{t+1}$ and becomes the latest market order. Before the end of $\textit{minute}_{t+1}$, the Order Model and Ensemble Model iteratively generate orders. The iterative generation of orders and order-batches guarantees a realistic balancing between market impact and controlled generation.
Refer to caption: x3.png

## 3 Experiments

This section evaluates MarS’s capability to provide realistic, controllable, and interactive simulations. We assess the realism of MarS by comparing the statistical properties (stylized facts) of historical market data with simulated data, demonstrating MarS’s ability to replicate key market phenomena. Next, we evaluate MarS’s controllability by generating target scenarios under predefined conditions, essential for applications such as stress testing and strategy optimization. We then explore interactive market dynamics within MarS using the TWAP agent, illustrating MarS’s realistic reflection of user interactions at the order level. Finally, we investigate the trade-off between control and interaction, evaluating MarS’s ability to balance generating controlled scenarios while accurately reflecting the market impact of interactive user inputs.

Throughout our experiments, we use the term “replay” to refer to replaying historical market data within MarS to validate the simulation against real-world events.

### 3.1 Realistic Simulations

To assess the realism of MarS’s market simulations, we compare simulated data against key stylized facts derived from historical market data (Vyetrenko et al., ; Coletta et al., ; Sherkar & Sen, ; Stillman et al., ). These stylized facts serve as robust benchmarks, ensuring that our simulations accurately reflect real-world market behaviors.
Several prevalent stylized facts are presented in Figure 4. Key findings are as follows:

- •
As the interval increases from 1 to 5 minutes, the distribution of log returns becomes more similar to a normal distribution (Aggregational Gaussianity).
- •
The auto-correlation of log returns rapidly decreases with increasing intervals (Absence of Autocorrelations).
- •
The simulation shows high volatility auto-correlation over periods (Volatility Clustering).

Figure: Figure 4: Illustration of Stylized Facts: The upper left panel displays the 1-minute log return distribution, the lower left panel shows the 5-minute log return distribution, the upper right panel depicts log return auto-correlation, and the lower right panel illustrates volatility auto-correlation.
Refer to caption: x4.png

In summary, MarS successfully replicates the stylized facts observed in historical data, thereby demonstrating its capability to produce highly realistic market simulations that are suitable for practical applications.

### 3.2 Controllable Simulations

We demonstrate MarS’s controllability by generating scenarios that mirror replays. An order batch is generated based on minute-level guiding signals from the replay curve, integrated with the order model within an ensemble model to generate trading orders. Figure 5 (Left) shows that the ensemble model closely follows the replay curve, whereas the order model shows less correlation.
Figure 5 (Left) illustrates that the simulated curves more accurately follow the replay curve, demonstrating a higher correlation, after the controlled refinement by the Ensemble Model during the order generation process.

We further compare the correlation between simulated and replay prices with different simulated trajectory numbers. Figure 5 (Right) shows the ensemble model, even with a single simulated trajectory, achieves higher correlation than the order model with 128 simulated trajectories, demonstrating its superior efficiency and effectiveness in generating controllable scenarios.

Figure: Figure 5: Left: Comparison of the order model and ensemble model for controlled scenario generation. Right: Correlation between simulated and replay prices with varying trajectory numbers.
Refer to caption: x5.png

### 3.3 Interactive Market Dynamics

Understanding market impacts is crucial for a wide range of applications. MarS allows for the simulation of market impacts by generating orders based on detailed order-level data. By interacting with a TWAP (Time-Weighted Average Price) agent, we demonstrate how MarS can realistically simulate the market impact of large trades within a short time window.

Figure 6 (Left) shows the market impact of a TWAP agent executing a large trade volume. The agent aims to purchase 100,000 units of shares within a 5-minute window, with the figure displaying the price trajectories and trading order details.
These results illustrate that MarS can effectively model the impact of trading strategies on market prices, providing valuable insights for market participants and aiding in the development of more robust trading strategies.

Figure: Figure 6: Left: Example of Market Interaction with a TWAP agent. The circle markers represent the orders submitted by the TWAP agent. Right: Correlation between simulated prices and replay prices with different simulation configurations.
Refer to caption: x6.png

### 3.4 Trade-off between Control and Interaction

We evaluate the ability of MarS to balance control and interaction using replay data exhibiting a $0.3\%$ to $0.5\%$ price change over 5 minutes. Our control target is to generate a similar price change scenario. When control is enabled, the ensemble model is guided by the replay curve. When interaction is enabled, a TWAP agent sells $20\%$ to $40\%$ of the replay volume within the same timeframe. We report the correlation between simulated and replay prices under different configurations.

Figure 6 (Right) illustrates the trade-off between control and interaction. Configurations with control but no interaction achieve the highest correlation scores ($0.47$), indicating model precision in replicating historical price movements. Introducing interaction reduces control precision ($0.47\rightarrow 0.33$), allowing for more realistic interactions in diverse applications and experiments.

## 4 Applications

In Sections 2 and 3, we demonstrated the formulation of diverse financial tasks as a conditional trading order generation problem. Our experiments confirmed that MarS is Realistic, Controllable, and Interactive, establishing it as a robust financial market simulator. This section explores potential downstream applications of MarS, further validating its foundational role in financial market simulation. We present practical financial tasks to illustrate: a) MarS’s capability to solve financial problems independently, and b) its utility as a simulation platform for other tasks. For a), we showcase Forecast and Detection tasks, and for b), we provide examples of ”What if” Analysis, and Reinforcement Learning Environment.

Here, we want to highlight that, analogous to text generation v.s. language modeling (Achiam et al., ; Abdin et al., ; Dubey et al., ), and video generation v.s. physical world decision making (Liu et al., ; Yang et al., ; ), we have constructed a unified task interface through conditional trading order generation diverse financial downstream tasks with MarS. This interface can transfer complex and diverse financial information into specific tasks.

Given that financial tasks are often abstract and highly domain-specific, we illustrate these tasks in bottom-right of Fig.1 for easier comprehension and summarize their input conditions in Table 1. We also compare the current methodologies with the new paradigm introduced by MarS to illustrate the “paradigm shift” across various types of financial tasks, as shown in Table 2.
The introduction and details of each task can be found in the subsequent sections.

**Table 1: The summary of input conditions for order generation of different applications. $*$ means the condition is optional and $[\ ]$ indicates that either of the specified conditions should be chosen.**
| Applications | Input Conditions |
| --- | --- |
| Forecasting | $\left(x_{0},\ldots,x_{m}\right),\textit{MTCH_R}$ |
| Detection | $\left(x_{0},\ldots,x_{m}\right),\textit{MTCH_R}$ |
| “What if” Analysis | [$\textit{DES_TEXT}],\left(x_{0},\ldots,x_{m}\right)^{*},[\left(\dot{x}_{i+1},<br>\ldots,\dot{x}_{i+j}\right)],\textit{MTCH_R}$ |
| RL Environment | $\textit{DES_TEXT}^{*},\left(x_{0},\ldots,x_{m}\right)^{*},\left(\dot{x}_{i+1}<br>,\ldots,\dot{x}_{i+j}\right),\textit{MTCH_R}$ |

**Table 2: The summary of how MarS reshape main-stream financial applications. $\operatorname{Diff}(\cdot,\cdot)$ is the difference between two market states for anomaly detection. $P(s_{t+1}|s_{t},a_{t})$ means the state transition given current state and action. Without an interactive environment, most existing financial RL works cannot model the realistic impact of market state caused by agent actions.**
| Applications | Current Methods | MarS |
| --- | --- | --- |
| Forecasting | sequence extrapolation | conditional generation |
| Detection | $\operatorname{Diff}(\textit{market}_{now},\textit{market}_{past})$ | $\operatorname{Diff}(\textit{market}_{now},\textit{simu-market}_{now})$ |
| “What if” Analysis | online exp., empirical formula | offline data-driven pipeline |
| RL Environment | finite data, fake $P(s_{t+1}|s_{t},a_{t})$ | infinite data, real $P(s_{t+1}|s_{t},a_{t})$ |

### 4.1 Forecasting

Forecasting is crucial in many financial applications, with market trend forecasting being a prime example. This task demands models that accurately capture and reflect market dynamics. Traditionally, direct forecasting models are used. In this section, we assess the effectiveness of our market simulation in predicting trends.

Following Ntakaris et al. (), we define the price change from $t$ to $t+k$ minute as follows:
$l=\left(\left(\frac{1}{n}\sum_{i=1}^{n}m_{i}\right)-m_{0}\right)/m_{0}$,
where $m_{0}$ is the mid-price at time $t$, $n$ is the number of orders between $t$ and $t+k$ minutes, and $m_{i}$ is the mid-price after the $i$th order event. The price change is categorized into three classes—up, down, and flat—based on the value of $l$, ensuring similar probabilities for each class. We compare our model with DeepLOB by Zhang et al. (), a well-known baseline. Figure 7 illustrates that LMM-based simulations significantly outperform DeepLOB, highlighting its superior market dynamics understanding. Additionally, the 1.02 billion-parameter model outperforms the 0.22 billion-parameter model, indicating that improved validation loss in scaling curve (Fig. 2) correlates with enhanced forecasting performance.

It is noteworthy that all forecasting targets can be calculated using simulated trajectories from MarS, whereas traditional direct forecasting models require separate training for each target. This underscores the significant advantage of simulation-based forecasting by MarS.

Figure: Figure 7: Trend Prediction Accuracy. We benchmark the predictive performance of our market simulation against DeepLOB. For each initial time point, the large market model executes 128 simulations, aggregating the outcomes to determine the final predicted class. The ground truth is obtained from historical data replay.
Refer to caption: x7.png

### 4.2 Detection

In addition to forecasting future trends, comprehending the current and recent market conditions constitutes a significant category of financial tasks.
Regulation particularly market abuse(^1^11[https://en.wikipedia.org/wiki/Market_abuse](https://en.wikipedia.org/wiki/Market_abuse)) regulation holds a crucial position in this type of tasks.

However, traditional methods for detecting illegal trading activities (e.g., insider trading (Meulbroek, ) and market manipulation (Putniņš, )) requires a significant amount of time and effort, often involving extensive data analysis and investigation. From the perspective of investors, it is hard for themselves to discern whether their financial assets were/are in an abnormal market.
In this section, we will use the example of market manipulation detection to demonstrate how MarS assists regulators and helps investors.

In Section 3, we have evaluated the realism of MarS in the normal market. So if the simulation realism of some stylized facts drops during a particular period, it indicates potential anomalies.
We collected several cases of market manipulation from the administrative penalty notices issued by the China Securities Regulatory Commission (CSRC)(^2^22[http://www.csrc.gov.cn](http://www.csrc.gov.cn)). For each stock, we gathered samples from an equal number of trading days before and after the manipulation occurred for comparison. We conducted simulations on samples from different periods.

Let’s take the spread metric as example. The spread is an important indicator of market liquidity, with a larger spread usually indicating poorer market liquidity. At time $t$, the spread $\delta$ is defined as:
$\delta_{t}=a_{t}-b_{t}$,
where $a_{t}$ is the best ask price and $b_{t}$ is the best bid price (Vyetrenko et al., ).
Comparison of spread in different periods around manipulation is shown in Figure 8. As observed in the figure, although MarS performs well in the spread metric overall, its performance during the manipulation period drops compared to the periods before and after.
The result illustrates that the spread during the manipulation period exhibits a heavier tail and a noticeable peak around $\delta=1000$ and distribution similarity of manipulation period is the lowest.
These observations are highly likely correspond to market manipulation behavior.
When manipulators leverage their capital and holding advantages to drive up stock prices or crash the market, they significantly consume market liquidity, causing the spread to widen and cluster at certain level.
However, this is an extremely abnormal phenomenon compared to most normal markets and constitutes a minority of the data in the model training set. Therefore, the performance of our model drops.
This provides a new approach to quickly detect abnormal activities such as market manipulation – by observing whether the performance of MarS suddenly drops in certain stylized facts.
Through this detection approach, MarS can potentially help more investors avoid market anomalies and assist more financial institutions to preserve market stability.

Figure: Figure 8: Spread distribution in different periods of market manipulation. Left: pre-manipulation period. Middle: manipulation period. Right: post-manipulation period. Spread during the manipulation period exhibits a heavier tail and a noticeable peak around $\delta=1000$. Additionally, compared to the pre- and post-period results, the distribution similarity drops during the manipulation period.
Refer to caption: x8.png

### 4.3 “What If” Analysis on Market Impact

One of the most important ‘what if’ topics in finance is analyzing market impact, the change in asset prices caused by trading activity, which is crucial for understanding and navigating financial markets, e.g., developing optimal trading strategies and detecting manipulation. Most existing research in this area is relied heavily on strong assumptions and empirical formulas (Zarinelli et al., ; Almgren et al., ; Gatheral, ; Gatheral et al., ; ), limited to costly and risky online experiments. In this section, we take the market impact as an example, showing how MarS can act as a reliable and powerful analysis platform and contribute to “what if” analysis. First, we explore the market impact data generated by MarS under various configurations and validate the consistency between the synthetic market impact and real market patterns. Having established the reliability of MarS in replicating real market behaviors, we then proceed to a more ambitious goal. Specifically, based on the generated data, we build data-driven pipeline to discover new laws of market impact and its higher-order sequential effect.

#### 4.3.1 Exploration and Validation of Generated Market Impact

We generate market impact data by the TWAP strategy with four different configurations: L1-P0.1, L1-P0.9, L5-P0.1, and L5-P0.9.
The configuration name LX-PY indicates that the aggressive price (AP) is askX and the maximum passive volume ratio (PVR) is Y. These agents are assigned to buy varying volumes over 5 minutes with different instructions and starting times.

We explored the market impact generated by these trading agents from 624k simulated trading trajectories. The key findings are summarized as follows:

- •
As shown in Figure 9 (left), despite the different configurations, the synthetic market impact follows a pattern similar to the Square-Root-Law market impact model: $\Delta=\alpha\times\sigma\sqrt{\frac{Q}{V}}$, where $\sigma$ is the volatility, $Q$ is the trading volume, $V$ is the total market volume, and $\alpha$ is a constant. The Square-Root-Law is widely regarded as the gold standard for testing market impact in the financial industry, known for its broad applicability and significance in capturing the relationship between trading activity and price changes (Moro et al., ; Lillo et al., ; Almgren et al., ).
- •
Agents with more aggressive configurations (L5-P0.1 and L5-P0.9) are expected to exhibit a larger market impact and achieve a higher fulfillment rate. Our simulations quantify their differences and confirm these assumptions, as illustrated in Figure 9 (left and middle).
- •
The agents generate both short-term and long-term market impacts, consistent with previous empirical studies (Bacry et al., ; Donier et al., ). We also observe that agents with a larger passive volume ratio generate less momentum after trading ends, as shown in Figure 9 (right).

These findings not only confirm the robustness of MarS but also highlight the reliability and convenience of using synthetic data generated by MarS for market impact analysis, allowing for in-depth exploration of market dynamics without the cost, risk, and time constraints associated with real-world experiments.

Figure: Figure 9: Market impact analysis. Left: Market impact by different configurations of the TWAP strategy. The impact linearly increases with the x-axis value $\sigma\sqrt{Q/V}$, showing a pattern similar to the Square-Root-Law model. Middle: Agents with more aggressive configurations achieve a higher fulfillment rate. Right: Trading agents generate both short-term and long-term market impacts. Specifically, agents with a larger passive volume ratio generate less momentum after trading ends.
Refer to caption: x9.png

#### 4.3.2 Discover New Laws of Market Impact

Market impact mechanisms are complex and difficult to predict accurately due to noise and randomness in observed data. Using synthetic data from MarS, we aim to establish a data-driven pipeline to uncover new interpretable laws. Specifically, we seek new factors beyond the Square-Root-Law that strongly influence market impact during trading, and we aim to learn a differential equation (DE) to model the high-order effect of market impact, the decay of market impact sequence over time after trades.

New factors of Market Impact:
To uncover new pre-trading factors influencing market impact, we employed symbolic regression, using classic volume and price factors before trading as the base dictionary. By applying genetic algorithms in multiple iterations, we sought to identify the most informative factors on synthetic market impact. The preliminary results were reviewed and refined by domain experts, leading to the discovery of three new factors that partially explain market impact:$\{$resiliency, LOB_pressure, LOB_depth$\}$. In Figure 10, we plot the relationships between market impact and the three new found factors.

Figure: Figure 10: Nonlinear effects of new factors on market impact.
Refer to caption: x10.png

Dynamics of Second-order Market Impact: The second order of market impact typically manifests as a gradually decaying sequence of price fluctuation after a trade. Traditional research has often relied on empirical formulas to model this dynamics (Gatheral et al., ; Donier et al., ; Bacry et al., ), but these approaches can struggle to capture the full complexity of real-world scenarios. To address this, we leverage generated market impact data to develop a more accurate, data-driven approach. Our method models the decay of market impact using an ordinary differential equation(ODE), which integrates both potential influencing factors and decay functions:

$$ $\displaystyle\frac{dY(t)}{dt}=\text{sum}(W\circ(X\otimes F^{\text{decay}}(t))) =\sum_{i=1}^{m}\sum_{j=1}^{n}W_{i,j}X_{i}F_{j}^{\text{decay}}(t)$ (1) $$

where $Y(t)$ is the after-trading market impact, $(X\in\mathbb{R}^{m})$ represents key influencing factors, such as volume, price, etc., and $F_{\text{decay}}(t):t\rightarrow\mathbb{R}^{n}$ includes possible decay functions, e.g., $F^{\text{decay}}(t)=[1/t,\ldots,1/sqrt(t)]$. Both $X$ and $F^{\text{decay}}(t)$ can be customized based on domain knowledge. $\otimes$ is the outer product, $\circ$ is the Hadamard product, $X^{T}\otimes F_{\text{decay}}(t)$ is a matrix with size $\mathbb{R}^{n\times m}$, representing interactions among factors and decay patterns, and $W\in\mathbb{R}^{n\times m}$ is the learnable weights of interactions. This learned ODE effectively explains how different factors, each with its own decay characteristics, contribute to the second-order effects of market impact. We set two decay functions and seven factors in the experiments. The left of Figure 11 illustrates the auto-correlation of the synthetic market impact decay, and trajectories predicted by the learned ODE, and the base ODE from empirical formulas(Gatheral et al., ; Curato et al., ). The right showing the learned weights $W$, demonstrating the importance of interaction pairs.

Figure: Figure 11: Learned ODE of second-order market impact and the interpretable interaction weights.
Refer to caption: x11.png

### 4.4 Reinforcement Learning Environment

The MarS environment, being both realistic and interactive, is ideal for training reinforcement learning (RL) agents. This environment accurately reflects an agent’s impact, provides realistic rewards, and facilitates training robust agents for the financial market. In this experiment, we aim to train a trading agent from scratch using MarS. The trading agent’s goal is to purchase a large volume within 5 minutes, optimizing both fulfillment rate and price advantage.

The trading agent’s state includes features such as remaining time, remaining volume, Limit Order Book (LOB) imbalance, and whether the period is passive or aggressive. The agent’s actions are based on a configurable Time-Weighted Average Price (TWAP) strategy, adjusting the maximum passive volume ratio (PVR) from {0, 0.1, …, 1} and aggressive price (AP) in {0, 1, 2, 3, 4, 5} for each trading part. A PVR of 0 indicates no passive volume during the passive period, while an AP of 0 means no aggressive order during the aggressive period.

The reward function is defined as:

$$ $\text{Reward}=\alpha\times\text{FulfillmentRate}+\text{PriceAdvantage}$ (2) $$

where $\alpha$ is 1 when the FulfillmentRate $\leq 0.95$ and decreases to 0 as the FulfillmentRate approaches 1.

For training, we used a batch size of 8192 and a learning rate of $4\times 10^{-5}$. The trading model was updated using a simple policy gradient algorithm (Sutton & Barto, ). The performance metric is the price advantage over our best-configured TWAP agent (L1-P0.9), measured in basis points (BP, 1/10000). Figure 12 shows the training performance of the trading agent. The agent’s performance improves from -6 BP to 2~6 BP during training. The observed fluctuations between 2~6 BP are attributed to the agent exploring various strategies between high and low fulfillment rates, resulting in corresponding variations in price advantage based on the current reward setting.

Figure: Figure 12: Training performance of the trading agent. The x-axis represents the number of update batches, and the y-axis is the price advantage over our best-configured TWAP agent (L1-P0.9), in basis points (BP). The agent’s performance improves from -6 BP to 2~6 BP during training, with fluctuations due to exploration between fulfillment rates.
Refer to caption: x12.png

This demonstration highlights that MarS is capable of training trading agents from scratch by leveraging its realistic and interactive simulation capabilities. A more comprehensive training design could yield even stronger performance.

## 5 Related Works

Financial Market Simulation. Prior to this tech wave of generative foundation models, researchers in the finance area had already envisioned the immense potential of powerful market simulations. Agent-based Modelling, particularly multi-agent systems, was initially employed to simulate order-driven markets (Chiarella et al., ; Byrd et al., ; Amrouni et al., ).
With the advancement of deep learning technologies, several works have emerged that adopt the world model paradigm to simulate Limit Order Book (LOB) markets (Takahashi et al., ; Li et al., ; Coletta et al., ; ; ). They mostly leveraged GANs (Goodfellow et al., ) to model the distribution of the LOB time series.
Only recently have there been some generators utilizing market micro-structure data, such as (Hultin et al., ; Nagy et al., ).
Among these, Nagy et al. () is most related to our work, particularly regarding the order model. It employs an auto-regressive model based on a Deep State Space Network (Rangapuram et al., ) to generate LOB and message flows. However, their work mainly focuses on LOB modeling. They demonstrates some realism stylized facts of the generated sequences but did not evaluate the model’s capability to address downstream financial tasks.
Beyond generating realistic order flows, our work aims to be a world simulator for financial markets and simulating the market effects of various and complex financial behaviors.
We propose MarS, a financial market simulation engine powered by a generative foundation model (LMM), addressing the domain-specific requirement of modelling orders’ market impact and controllable generation with high realistic.
By formulating diverse financial market tasks as a conditional trading order generation problem, we demonstrate the capability of MarS in real financial market.

Foundation Model. Foundation models are those trained on broad data that can be adapted to a wide range of downstream tasks. The Stanford institute (Bommasani et al., ) first created and popularized this term.
The release of GPT-3 (Brown, ) demonstrated the powerful benefits of training large auto-regressive language models (LLM) on extensive corpus (Abdin et al., ; Achiam et al., ; Dubey et al., ).
Besides, numerous foundation models have emerged in the fields of computer vision (CV) and multimodal area (Rombach et al., ; Brooks et al., ; Liu et al., ).
Recently, real-world simulators and industry-specific large models are becoming popular research topics in this field.
Real-world simulators aim to achieve real-world simulation through the unified goal of video generation, addressing various tasks in fields such as autonomous driving, robotics, and gaming (Liu et al., ; Zhu et al., ; Yang et al., ; ). However, they primarily focus on simulating the physical world. The order-driven financial market is an exemplary virtual world with different operating principles. To the best of our knowledge, we are the first to build an financial world simulator.
Industry-specific large models primarily focus on fields such as biomedical (Moor et al., ), law(Huang et al., ) and finance.
In the financial domain, most large models are Financial LLMs, which either pre-train LLMs on financial corpora (Wu et al., ; Zhang & Yang, ) or fine-tune them (Xie et al., ; Zhang et al., ; William Todt, ; Yang et al., ) to tackle financial NLP tasks or multimodal tasks (Bhatia et al., ; Xie et al., ) including sentiment analysis, text classification, question answering, and etc..
However, beyond text, there is an even larger and more information-rich corpus in the financial world – trading orders. We propose a Large Market Model (LMM), which, for the first time, reveals the scaling law on trading orders. We takes the first step toward building a generative foundation model as a world model for the financial market. We hold the belief that, with MarS as the shovel, the extensive order-level data undoubtedly represent a significant gold mine.

## 6 Conclusion

We propose MarS, an order-level fine-grained realistic financial market simulation, powered by our a generative foundation model Large Market Model. As far as we know, this paper is the first attempt to evaluate the scaling capability in financial order generation. The evaluation of LMM’s scaling law demonstrate the potential of further enhancement of the order generation for financial markets. We also summarized the three key characteristics (i.e., realistic, controllable and interactive) for various financial downstream tasks and designed a framework to address these characteristics. Four types of downstream tasks are demonstrated in the application which we hope inspire the community and industry for this promising direction of financial world model and simulation for various downstream applications.

## Acknowledgements

We would like to express our sincere gratitude to Chengqi Dong for his invaluable contribution to this research. His meticulous analysis of market impact data and exploration of new factor discovery have significantly enhanced our understanding of market impact studies.

## Disclaimer

Users of the market simulation engine and the code should prepare their own agents which may be included trained models built with users’ own data, independently assess and test the risks of the model in a specify use scenario, ensure the responsible use of AI technology, including but limited to developing and integrating risk mitigation measures, and comply with all applicable laws and regulations. The market simulation engine does not provide financial opinions, nor is it designed to replace the role of qualified financial professionals in formulating, assessing, and approving finance products. The outputs of the market simulation engine do not reflect the opinions of Microsoft.

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: The main questions and suggestions are derived from the identified weaknesses.

The paper should be restructured by including more specific key definitions and design decisions, including ML-specifc (relevant for the ICLR audience) from the Supplementary Materials into the main paper.

"RL-agent training tasks" is mentioned twice in the paper (p. 8). It would help to link this term to Section 4.4, for improved clarity and readability. Also, discussing the differences between MaRs/LMM and DeepLOB would improve the paper. Clearly defining the synthetic data and synthetic market impact (rather than referring to them indirectly in the main part of paper) would also be helpful.

In addition, it would help for the authors to address reproducibility, in terms of code and data.

Overall, the suggested changes would improve the rigor, clarity and overall contribution of the paper, as well as its suitability for the ICLR audience.

There are some minor spelling/ typo errors, e.g.: "these information concludes" (p. 5); "with constrains" (p. 28); Eq.equation (p.28)
soundness: 3
strengths: The paper makes a contribution in a highly relevant application domain, i.e. realistic financial market simulation frameworks. The methodology is adequate, and experiments and results are included in support of the statements and contribution claims. The main part of the paper is focused on LLM and MaRs, presenting the design and implementation decisions, and a detailed description of the experiments and results. The paper includes evidence of the LLM's scalability across data size and model complexity. In addition, MaRs enables more realistic, interactive and controllable order generation. A range of different scenarios illustrate the applicability of MaRs to key domain-specific tasks such as forecasting, detection, analysis, and agent training, thus demonstrating its contributions towards more realistic financial market modelling and simulation frameworks.
summary: This paper makes several contributions: (i) it designs, implements and evaluates Large Market Model (LMM), an order-level generative foundation model, for financial market simulations; (ii) a novel financial Market Simulation engine (MarS), based on LMM, that enables more realistic, domain-specific interactive and controllable order generation. The paper includes evidence of LMM's strong scalability across data size and model complexity, and of MarS's advancements towards more realistic, interactive and controllable order generation with market impact. Various scenarios illustrated the application of MarS for forecasting, detection, analysis, and agent training, thus demonstrating its contributions towards more realistic financial market modelling and simulation frameworks.
weaknesses: The current structure of the main part of the paper prioritises a high-level presentation of LLM and MaRs, and the applicability of the proposed solution to four relevant use cases. The MaRs design and features (Section 2) are also presented at a high level, with insufficient rigour in the problem definition (Section 2.1) -- which may not be known to a ML audience. It is not clear why, for example, being able to provide a text-based description of the desired market scenario, would guarantee controllability (the definition of controllability on page 2 is fairly vague). Similarly, the assumptions made/ requirements about the user-injected orders are not specified. The language is ambiguous in places, e.g. "any possible market condition" (p. 2); "often using recent real orders" (p. 3). More technical detail could be included in Section 2.1.2, for self-contained, rigorously specified problem and solution,  and to support the claims made in this section.

It would help to better define the control signals, and discuss their effectiveness for increasing correlation scores.

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confidence: 4
contribution: 3
initial_rating: 3
presentation: 2
questions: - In the section B.2, the author mentioned the index could uniquely identify a limit order. Could the authors provide a concrete example?

- In the order-batch sequence modeling part, is there any mechanism/constraint to prevent the number of cancel order be greater than the outstanding orders? If such scenario happens, how the will the framework cope with it?

- In the section 3.3, I am not following why the interaction ability is evaluated using the correlation. Could the authors elaborate?
soundness: 2
strengths: 1. A major strength of this paper is its algorithmic innovation in using order book data tokenization and an RGB-like tensor representation, which importantly bridges market simulation with advances in language and vision modeling.

2. The paper introduces a timely topic by connecting LOB market simulation with generative modeling.
summary: In this paper, the authors propose a financial market simulation framework, MarS, powered by a large market model (LMM) trained on real-world limit order book (LOB) data. They introduce two key algorithmic innovations: order sequence modeling, which tokenizes the LOB data, and order batch sequence modeling, which converts it into a tensor representation similar to the RGB format in image processing. These techniques connect LOB market simulation to recent advances in the field. In their experiments, the authors demonstrate that the LMM follows the scaling law for model and training data size, showcasing potential use cases for the framework.
weaknesses: 1. The paper’s reproducibility would benefit from providing additional critical details about the method and implementation.

  - In Section 2.1.1, the authors outline that conditional trading order generation requires several hyperparameters, such as DES_TEXT for general market description and MTCH_R for specifying the matching rule for trading orders. However, the experimental section does not provide configuration details for these hyperparameters in relation to the obtained results.
  
  - While the authors provide sufficient detail on order sequence modeling and order batch sequence modeling, the training process for the ensemble model lacks detailed illustration, and further illustration on how the two methods are combined within the ensemble would be beneficial.

  - The authors mention that the LMM is trained on real-world market data; however, they do not provide data processing details. For example, real-world LOB data includes various order types (e.g., stop-loss orders, limit orders, market orders) that may arrive asynchronously in the market, yet the paper does not specify how these orders are mapped to the bid and ask sides as described.

2. More comprehensive evaluations are needed to demonstrate the authenticity of the simulated market. Although the authors include three tests of stylized facts, further testing to show that the framework conforms to additional stylized facts would strengthen its credibility. Please see "Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative finance, 1(2), 223." for details. Ideally,  multiple iterations and providing confidence intervals for the measures are preferred.

3. Some of the experiments are not necessarily good demonstrations about the model strength and their design need to be further improved.

  - In the 4.2 detection experiment, 1) the manipulation seems can be easily identified due to anomaly in the distribution tail without resorting to the simulation 2) the distribution similarity need to be clearly defined and demonstrate it is statistical different from the others 3) the author may want to compare with other anomaly detection algorithms.

  - The factor analysis is not a good application example because 1) it could also performed on real world data. 2) the simulated market may not good representation about the real-world market if only three stylized facts are satisfied.

4. The paper’s clarity would benefit from further improvement. Since order sequence modeling and order-batch modeling are two key innovations, the description of these methods should be included in the main content rather than in the supplementary materials.

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confidence: 3
contribution: 3
initial_rating: 8
presentation: 4
questions: (1) Order-sequence model 
The order-sequence model uses an autoregressive approach to capture patterns within the order book, aiming to predict subsequent orders. However, the diversity of trading strategies among market participants complicates this task, often making the next order seemingly random and unpredictable. For instance, a momentum trader might buy following a price increase, anticipating continued upward movement based on the persistence of price trends. Conversely, a mean reversion trader sees a price rise as a selling opportunity, expecting prices to normalize back to the mean, counter to the current trend. Could you provide literatures or evidences in your experiments supporting a relationship between orders?

(2) Diffusion model
In Figure 1, a diffusion model is introduced. Could you explain the rationale behind this choice and how the diffusion model is utilized in this context?
soundness: 3
strengths: The paper introduces a Large Market Mode and the MarS engine, which use order-level generative foundation models for simulating financial markets. This is an advancement research expanding on traditional statistical and agent-based models, providing promissing resolution, interactivity, and realism.

This paper is well-written, clear, and consice. It begins by identifying a specific research gap, then clearly states the proposed solution, and explains how it functions. Additionally, the paper describes potential downstream applications and further research opportunities, all within a well-organized logic chain.
summary: This paper introduces a generative model designed to simulate realistic order-levels scenarios in financial markets. It uses a large language model to analyze the current market environment, taking this information within a proposed large market model. The model comprises two main components: an order-batch model that captures temporal patterns and an order model that addresses the sequential nature of market orders. These orders are then interactive with user's injection in a simulated in a simulated clearinghouse environment.

To validate the model, the paper conducts tests on stylized facts to ensure realistic simulation outcomes and applies the square-root law to assess interactive simulation capabilities. It also evaluates the model’s scalability in large-scale market scenarios.

Following validation, the model is applied in four downstream applications: forecasting, anomaly detection, what-if scenario analysis, and training datasets for agent-based models.

The paper contributes a model for simulating realistic financial markets, which has potential for application across various downstream scenarios.
weaknesses: (1) Time Interval. 
The model discussed in this paper simulates market at the minute level, whereas in actual financial markets, transactions can occur at the nanosecond level. There could be challenges in accurately capturing the extreme volatility and rapid decision-making. Specifically, using a closed-source LLM engine might introduce limitations due to rate constraints. In contrast, this paper employs an open-source engine, which necessitates careful consideration of its reasoning and inferential capabilities to ensure it can effectively model the high-speed dynamics of financial markets. Does the MarS model have the design capability and flexibility to increase the level of trading time intervals?

(2) Multi-order book correlation.
In the design of large market models, the two primary approaches are the order-sequence model and the order-batch model, which capture temporal correlations and patterns. Additionally, in the conditional generation process, it seems to focus solely on a single order book. Considering that markets consist of multiple order books and each asset is significantly influenced by others as well as the market environment, how can the model effectively capture the correlations between different order books?

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 4
questions: - What does "MTCH R" refer to exactly? It’s not clear how a conditional model should interpret a constraint on the "feasible space for each order".

- Is the "SIMULATED CLEARING HOUSE" simply an exchange engine simulating a double auction market, or is it something else? It seems to be the latter. 

- For the order-batch model, which generates orders at the end of each minute, is this the smallest reaction time of the simulation in response to orders? Or does the model plan a minute ahead (a batch of orders) and then refine (by conditioning) that batch using the Order model? How exactly does the condition in Figure 3 function here?

- In Figure 5a, the market replay appears to be shifted (due to buy orders). Is this intentional? Using the replay series as a control? I suggest showing this experiment with a shaded area over multiple simulations with similar buy and sell orders (similar to Figure 17).

- Why is MarS assumed to have a "real" transition distribution P(s | s, a) in Table 1? 

- In Section 4.2, the detection approach is interesting, but I’m curious whether the observed difference in distribution similarity (computed how?) is statistically significant. Are stressful trading days or shocks interpreted as manipulation as well? Before claiming this approach is feasible, it would be helpful to see the average difference in spread distribution over multiple days or periods.

- In Figure 19b, the market impact appears to be permanent. Is it true? What happens if we extend the simulation period?

- How does the model adapt to different markets (without re-training)? For example, Chinese markets generally differ significantly from U.S. markets in terms of liquidity and frequency.
soundness: 2
strengths: - The paper addresses an important and complex challenge, moving a step towards a more general and powerful generative model for limit order book simulation.
- The authors use for the first (to the best of my knowledge) the LLaMA2 architecture for order flow generation, showing also the potential of this architecture with more data and model parameters (Fig.2) 
- The downstream tasks are quite interesting and useful.
- The paper is well written and easy to follow.
summary: This paper presents a market simulation environment driven by a generative model that dynamically produces new market orders, based on the current market context and the historical order flow. This enables a responsive, interactive simulation of market dynamics. The model aims at supporting various applications, including forecasting, anomaly detection, market analysis, and agent training.

The core generative model, named the Large Market Model (LMM), is designed on the idea of a "foundation model for financial market simulation, akin to language modeling in the digital world".
weaknesses: Overall, I believe the paper has significant merit and I tend to recommend acceptance (and increase my score). However, I have some concerns, particularly regarding reproducibility. I would encourage the authors to make efforts to improve this aspect of their framework.

Below, I outline my main concerns and questions:
- Key details needed for reproducibility, such as code or datasets, are missing.
- Given that this is a conference on representation learning, more discussion on the embedding of orders and the LOB state would be valuable. For instance, are all possible order prices linearly discretized into the range [0, 32)? Are price outliers excluded? does the model use absolute prices or the distance from the midprice?
- What are the training and simulation times? The latter is particularly crucial for the proposed tasks, as generating a few hours of price paths requires thousands of generated orders.
- A discussion of limitations is missing. For example, unlike text with a relatively fixed vocabulary, a fixed embedding for orders might reduce adaptability across different markets?
(see also questions)

Minor:
- Some essential details should appear in the main paper, such as the dataset used and the authors’ use of a LLAMA2 architecture.
- In line 40, when the authors briefly discuss existing market simulation models, it would be helpful to include citations. This will guide readers interested in statistical or agent-based models to relevant literature.
- There is occasional overuse of non-technical terms, such as “gold mine of data,” and some paragraphs (e.g., lines 236 and 240), which are also capitalized. Are these intended as citations?
- In paragraph 2.1.2, clearer spacing or breaks between components would improve readability.
- Typo on line 384 (“classesup…”).
- The diffusion model in Figure 1 is not explained or discussed.

Meta-review: This paper describes a generative model for simulating financial market data. All reviewers found the paper to be addressing an interesting and important topic and that it was well argued and supported.

Decision: Accept (Poster)