A multi-factor model for improved commodity pricing: Calibration and an application to the oil market

ArXiv ID: 2501.15596 “View on arXiv”

Authors: Unknown

Abstract

We present a new model for commodity pricing that enhances accuracy by integrating four distinct risk factors: spot price, stochastic volatility, convenience yield, and stochastic interest rates. While the influence of these four variables on commodity futures prices is well recognized, their combined effect has not been addressed in the existing literature. We fill this gap by proposing a model that effectively captures key stylized facts including a dynamic correlation structure and time-varying risk premiums. Using a Kalman filter-based framework, we achieve simultaneous estimation of parameters while filtering state variables through the joint term structure of futures prices and bond yields. We perform an empirical analysis focusing on crude oil futures, where we benchmark our model against established approaches. The results demonstrate that the proposed four-factor model effectively captures the complexities of futures term structures and outperforms existing models.

Keywords: Four-factor model, Stochastic volatility, Convenience yield, Kalman filter, Commodity pricing

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical methods including multi-factor affine models, stochastic differential equations, Kalman filtering, and PDE solutions, indicating high mathematical complexity. It also demonstrates strong empirical rigor through in-sample and out-of-sample testing on crude oil futures data, benchmarking against established models, and incorporating bond yield estimation for practical applicability.

  flowchart TD
    A["Research Goal: Improve commodity pricing"] --> B["Proposed Four-Factor Model<br>Spot Price, Stochastic Volatility,<br>Convenience Yield, Stochastic Interest Rates"]
    B --> C["Methodology: Kalman Filter Framework<br>Simultaneous Parameter Estimation"]
    C --> D["Data & Inputs<br>Crude Oil Futures & Bond Yields"]
    D --> E["Computational Process<br>Joint Term Structure Estimation"]
    E --> F["Key Findings: Outperforms Existing Models<br>Captures Term Structure Complexities"]