Forecast

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. We compare our model with DeepLOB. The figure above shows the trend prediction accuracy, illustrating 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 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.

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 regulation holds a crucial position in this type of tasks. Based on MarS's realism in a normal market, a straightforward principle for anomaly detection is that a quick drop in simulation realism metrics indicates potential anomalies. We collected replay samples before (left), during (middle) and after (right) the manipulation, and conducted simulations by MarS simultaneously. The results are shown on figure above. While MarS generally performs well to simulate the normal market, its performance drops during the manipulation, showing a heavier tail and a peak around spread=1000. These anomalies likely correspond to market manipulation, where manipulators significantly impact liquidity, widening the spread. These anomalies, less frequent in normal markets, lead to a performance drop in MarS, suggesting a new detection approach by monitoring such similarity drops. Consequently, MarS helps investors avoid anomalies and assists institutions in maintaining market stability.

"What IF" Analysis on Market Impact

One of the most important ''What if'' topics in finance is to analyze market impact, the change in asset prices caused by trading activity. We attempt to leverage the synthetic data to build data-driven pipeline to discover new laws to explain market impact and its long-term dynamics.

We explore the potential market impact using a "What IF" analysis by simulating the effects of different trading strategies under various configurations. Specifically, we use the TWAP strategy with four distinct 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. Our "What IF" analysis yields the following insights:

• As shown in figure left-above, despite the different configurations, the synthetic market impact follows a pattern similar to the Square-Root-Law model, showing consistency with known market impact behavior.
• 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 the figure middle-above.
• The agents generate both short-term and long-term market impacts in MarS, as shown in the figure right above, similar to observations studied in previous empirical work. We also observe that agents with a larger passive volume ratio generate less momentum after trading ends.

Market impact is notoriously difficult to predict due to noise and randomness in observed data. Using MarS’s synthetic data, we perform a "What IF" analysis to explore new, interpretable laws beyond the traditional Square-Root-Law. By constructing a data-driven pipeline and applying genetic algorithms with symbolic regression, we identify three significant factors {resiliency, LOB_pressure, LOB_depth} that strongly influence market impact during trading. These factors provide a deeper understanding of how market conditions can shape price movements and execution behavior over time, offering a more nuanced view of trading dynamics.

The long-term market impact, also known as price impact trajectory, typically manifests as a gradually decaying sequence of price fluctuation after a trade. We develop an Ordinary Differential Equation (ODE) model (as shown in Equation ) below to capture the decay of market impact after trades are executed. Our method models the decay of market impact using an ordinary differential equation(ODE), which integrates both potential influencing factors and decay functions:

where $Y(t)$ is the long-term market impact, $X \in \mathbb{R}^m$ is the factor group, such as volume, price, etc., and $F^{\text{decay}}(t): t \rightarrow \mathbb{R}^n $ includes possible decay functions, e.g., $ [1/t, \ldots, 1/\sqrt{t}]$. $X$ 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 interaction weight. Equation can explain how factors with different decay patterns contribute to the long-term market impact. The figure left-above illustrates the auto-correlation of the synthetic market impact decay, and trajectories predicted by the learned ODE, and the base ODE from empirical formulas. The figure right-above shows the learned weights $W$, demonstrating the importance of interaction pairs of two decay functions and seven factors, which can help to deepen our understanding of the long-term market impact.

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 above figure shows the test 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. 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.

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-injected 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 systems, analysis platforms, and agent training environments.

Scaling Law in Large Market Model

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.

Controllable Simulations