Hierarchical Graph Learning for Calendar Spread Strategies in Commodity Futures Markets

2026-06-24

AI Summary

This study addresses the limitation of existing calendar spread strategies in commodity futures, which typically fail to explicitly model the expiration-date dependencies among contracts. To overcome this, the authors propose a hierarchical graph learning framework that constructs a two-layer graph structure—comprising underlying assets at the upper layer and specific futures contracts at the lower layer—and captures inter-contract relationships through cross-level edges. Leveraging graph neural networks, the model forecasts price dynamics and translates these predictions into trading signals via a dedicated position-mapping mechanism. This work represents the first application of hierarchical graph learning to calendar spread trading, explicitly encoding cross-contract expiration dependencies. Empirical results on CME commodity futures data demonstrate that the proposed approach significantly outperforms benchmark models in both predictive accuracy and risk-adjusted returns, confirming the efficacy of the designed graph architecture and trading strategy.

Abstract

Commodity futures can be represented hierarchically, with underlying assets at the upper level and individual futures contracts at the lower level. Entities at each level can be connected by edges reflecting inherent correlations, with cross-level edges capturing contract-to-underlying asset connections. Building on our observations of these structures, we propose a hierarchical graph learning approach for calendar spread (CS) strategies in commodity futures markets, addressing two significant gaps in the machine-learning literature: (i) the absence of learning-based methods for CS strategies in futures markets, and (ii) the lack of consideration of maturity-dependent interrelationships across commodity futures. We first establish the efficacy of CS strategies by analytically showing that CS strategies can possess higher risk-adjusted returns, measured by the information ratio, and lower risk, measured by variance and delta, than long-only strategies. We then introduce a method to convert learning-based predictions into CS positions. Next, we develop a hierarchical graph learning method that predicts futures price movements by utilizing the maturity-dependent interrelationships, thereby yielding a CS trading algorithm. Empirical results on commodity futures markets traded on the Chicago Mercantile Exchange Group demonstrate that our method outperforms benchmark models in both prediction and trading performance. We find that maturity-dependent interrelationships across commodity futures are instrumental in prediction and that CS trading based on hierarchical graph learning is effective for statistical arbitrage.

Problem

• calendar spread
• commodity futures
• maturity-dependent interrelationships
• machine learning
• hierarchical structure

Innovation

• hierarchical graph learning
• calendar spread
• commodity futures
• maturity-dependent interrelationships
• statistical arbitrage