Affine Diffusion Modeling of Commodity Futures Price Term Structure

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Title: Affine Diffusion Modeling of Commodity Futures Price Term Structure
Author: Tian, Yanjun
Advisors: Nick Piggott, Committee Member
Peter Bloomfield, Committee Member
John Seater, Committee Member
Paul Fackler, Committee Chair
Abstract: Diffusion modeling of commodity price behavior is important for commodity risk management. This research seeks to improve upon the existing commodity diffusion models by incorporating stochastic volatility and seasonality through the affine diffusion framework. In particular, it evaluates affine diffusion models' performance at modeling commodity futures price term structure. Six affine diffusion models are studied in this research. They are one, two, three-factor Gaussian model and one, two, three-factor stochastic volatility model with a single stochastic volatility factor. Seasonality is modeled by allowing the forcing terms of the instantaneous drift and the instantaneous covariance to be seasonal. Model estimation is done through Q-MLE, for which the state variables are filtered through the Kalman Filter. To build the connection between affine diffusion models and known market regularities, affine state variables are interpreted. Factor interpretations used include the log of the spot price, a spot drift factor, and a spot variance factor. Empirical analysis covers models' performance at fitting and predicting futures price term structures; behavior of the interpretable models; and model stability. Empirical studies are applied to the corn and the unleaded gasoline markets. The following conclusions can be drawn from both markets: 1. For the purpose of modeling futures price dynamics alone, stochastic volatility models have no advantage over Gaussian models; 2. At least two factors are needed to adequately model commodity futures price term structures; the advantage of three-factor models, which is better capturing the curvature of the term structures, become evident under extreme market conditions; 3. State independent seasonality modeling is effective under most market conditions, but under extreme market conditions, seasonality can be mis-represented and it is the source of big measurement errors and prediction errors. 4. Two and three-factor affine diffusion models are able to generate model behavior that is consistent with known market regularities.
Date: 2003-07-28
Degree: PhD
Discipline: Economics

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