Efficient Triangular Arbitrage Detection via Graph Neural Networks (2502.03194v1)

Abstract: Triangular arbitrage is a profitable trading strategy in financial markets that exploits discrepancies in currency exchange rates. Traditional methods for detecting triangular arbitrage opportunities, such as exhaustive search algorithms and linear programming solvers, often suffer from high computational complexity and may miss potential opportunities in dynamic markets. In this paper, we propose a novel approach to triangular arbitrage detection using Graph Neural Networks (GNNs). By representing the currency exchange network as a graph, we leverage the powerful representation and learning capabilities of GNNs to identify profitable arbitrage opportunities more efficiently. Specifically, we formulate the triangular arbitrage problem as a graph-based optimization task and design a GNN architecture that captures the complex relationships between currencies and exchange rates. We introduce a relaxed loss function to enable more flexible learning and integrate Deep Q-Learning principles to optimize the expected returns. Our experiments on a synthetic dataset demonstrate that the proposed GNN-based method achieves a higher average yield with significantly reduced computational time compared to traditional methods. This work highlights the potential of using GNNs for solving optimization problems in finance and provides a promising approach for real-time arbitrage detection in dynamic financial markets.

• The paper demonstrates a GNN-based approach that optimizes triangular arbitrage detection in currency networks.
• It integrates graph representation and deep Q-Learning with a relaxed loss function to improve computational efficiency and yield.
• Experimental results show an average yield of 6.3% with evaluation times reduced from 320ms to 147ms compared to traditional methods.

Efficient Triangular Arbitrage Detection via Graph Neural Networks

The paper "Efficient Triangular Arbitrage Detection via Graph Neural Networks" (2502.03194) introduces a novel method for detecting triangular arbitrage opportunities in currency exchange networks using Graph Neural Networks (GNNs). This method aims to enhance the efficiency and efficacy of identifying profitable trading strategies compared to conventional techniques like exhaustive search algorithms and linear programming.

Introduction and Context

Triangular arbitrage exploits discrepancies in currency exchange rates to yield profits. Traditional detection methods, including LP solvers and heuristic algorithms, often encounter drawbacks related to computational inefficiency. These methods struggle in dynamic markets where rapid analysis is crucial. The paper sets forth a GNN-based approach wherein the currency exchange is modeled as a graph, with nodes representing currencies and edges representing exchange rates. GNNs, known for their proficiency in handling graph-structured data, present an opportunity to capture the complex interrelationships among various currencies, providing a robust framework for real-time arbitrage detection.

Problem Definition

Linear Programming in Arbitrage

The paper describes the triangular arbitrage problem as a linear programming task. It involves optimizing a linear objective function under constraints that reflect real-world currency trading scenarios. The formulation accounts for exchange rates in a graph-like structure, facilitating the utilization of GNNs to map out strategies that maximize profit while adhering to these constraints.

Graph Representation

By representing the currency exchange network as a directed graph $G = (V, E)$, with currencies as nodes and exchange rates as directed edges, the GNN approach effectively transforms the arbitrage detection task into a graph-based optimization problem. This representation enables the implementation of sophisticated learning strategies to discern advantageous trading paths within the network.

Methodology

GNN Architecture

The architecture comprises multiple layers encompassing an input layer, hidden layers with message-passing capabilities, and an output layer. The message-passing mechanism updates node features iteratively, capturing the interdependencies of the currencies represented in the graph. The output layer then generates optimized trading strategies that maximize the expected yield from triangular arbitrage.

Loss Function Relaxation

A critical innovation is the introduction of a relaxed loss function that incorporates penalty terms for constraint violations. This relaxation enhances learning flexibility and accelerates convergence, enabling the GNN model to efficiently balance the trade-off between profit maximization and constraint satisfaction.

Integration of Deep Q-Learning

Further extending its capabilities, the method integrates principles from Deep Q-Learning, which optimizes expected returns by iteratively adjusting the trading strategy based on feedback from the associated currency exchange graph.

Experimental Results

Experiments conducted on synthetic datasets demonstrate that the proposed GNN-based method achieves an average yield of 6.3%, outperforming both the Bellman-Ford algorithm and traditional LP solvers in terms of computational time and profitability. Compared to an LP solver, the GNN method delivers similar or improved yields with notably reduced computational demands—147ms versus 320ms per network evaluation, respectively.

Conclusion and Future Directions

The paper concludes that the GNN-based approach to triangular arbitrage provides substantial improvements in speed and yield, making it well-suited for real-time applications in financial markets. Future research directions may include optimizing GNN architectures, validating the approach with real-world trading data, and exploring multi-step arbitrage detection. Expanding the model's scalability and integrating complementary machine learning techniques could further enhance its efficacy in complex financial applications.

Overall, the integration of GNNs and deep reinforcement learning into the financial optimization domain offers a promising pathway for developing advanced arbitrage detection methodologies that are both computationally efficient and economically beneficial.