This paper presents a novel multivariate mean-reverting jump-diffusion model that incorporates correlated jumps and seasonal effects to capture the complex dynamics of commodity prices. The model also accounts for the interplay between price volatility and convenience yield, offering a comprehensive framework for commodity futures pricing. By leveraging the Feynman–Kac theorem, we derive a partial integro-differential equation for the conditional moment generating function of the log price, enabling an analytical solution for pricing commodity futures. This solution is validated against Monte Carlo simulations, demonstrating high accuracy and computational efficiency. The model is empirically applied to historical futures prices of natural rubber from the Thailand Futures Exchange. Key parameters—including commodity price dynamics, convenience yields, and seasonal factors—are estimated, revealing the critical role of jumps and seasonality in influencing market behavior. Notably, our findings show that convenience yields are negative, reflecting higher inventory costs, and tend to increase with rising spot prices. These results provide actionable insights for traders, risk managers, and policymakers in commodity markets, emphasizing the importance of correlated jumps and seasonal patterns in pricing and risk assessment.