Ribeiro, Diana (2004) Models for the price of a storable commodity. PhD thesis, University of Warwick.

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Abstract

The current literature does not provide efficient models for commodity prices and
futures valuation. This inadequacy is partly due to the fact that the two main streams
of the literature - structural models and reduced form models - are largely disjoint. In
particular, existing structural models are developed under rigid discrete time framework
that does not take into account the mean-reverting properties of commodity prices.
Furthermore, most of the literature within this class does not analyze the properties of the
futures prices. Current reduced-form models allow cash-and-carry arbitrage possibilities
and do not take into account the dependence between the spot price volatility and the
inventory levels.
This thesis investigates three new models for the price of a storable commodity
and futures valuation. Specifically, we develop a structural model and two reduced-form
models. In doing so, we expand the leading models within each of the two streams of
the literature, by establishing a link between them. Each of these models provide an
advance of their type.
This study makes several contributions to the literature. We provide a new
structural model in continuous time that takes into account the mean reversion of commodity
prices. This model is formulated as a stochastic dynamic control problem. The
formulation provided is flexible and can easily be extended to encompass alternative
microeconomic specifications of the market. The results provide an optimal storage
policy, the equilibrium prices and the spot price variability. We also develop a numerical
method that allows the construction and analysis of the forward curves implied by this
model. We provide a separate analysis considering a competitive storage and considering
a monopolistic storage. The results are consistent with the theory of storage. Furthermore,
the comparison between monopoly and competition confirm the economic theory.
We developed a simple reduced-form model that focuses both on the mean reverting
properties of commodity prices and excludes cash-and-carry arbitrage possibilities. This
model is compared with a standard single-factor model in the literature. This new model
adds two important features to the standard model and motivates the development of a
more sophisticated reduced-form model. Accordingly, the last model developed in this
thesis is a reduced-form model. It is a two-factor model that represents the spot price
and the convenience yield as two correlated stochastic factors. This model excludes
cash-and-carry arbitrage possibilities and takes into account the relationship between the spot price volatility and the inventory level. We find an analytical solution for the
futures prices. This model is tested empirically using crude oil futures data and it Is
compared with one of the leading models in the literature. Both models are calibrated
using Kalman filter techniques. The empirical results suggest that both models need to
be improved in order to better fit the long-term volatility structure of futures contracts.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	H Social Sciences > HB Economic Theory
Library of Congress Subject Headings (LCSH):	Prices -- Econometric models, Commodity futures -- Econometric models, Commercial products -- Storage
Official Date:	May 2004
Dates:	Date Event May 2004 Submitted
Institution:	University of Warwick
Theses Department:	Warwick Business School
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hodges, Stewart D. ; Whalley, Elizabeth
Sponsors:	Fundação para a Ciência e a Tecnologia (FCT) ; Warwick Business School
Extent:	xvi, 212 p.
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/4063

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