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08.08.2019 | Original Research

Commodity Spot and Futures Prices Under Supply, Demand, and Financial Trading: Single Input–Output Model

verfasst von: Katsushi Nakajima

Erschienen in: Asia-Pacific Financial Markets | Ausgabe 1/2020

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Abstract

This study analyzes the relationships of commodity spot and futures prices with convenience yield. Convenience yield is received by the owner of a spot commodity but not by the owner of the right to the commodity (e.g., futures). This is the first study to explicitly model commodity spot and futures prices using firms and speculators (i.e., supply and demand of a commodity). We found that spot and futures prices are related to convenience yield. Based on this we were able to identify the structure of convenience yield, which can be decomposed into two components: yield and cost. When speculators are introduced, the spot commodity price is the discounted futures price minus the present value of the marginal storage cost plus the convenience yield on the spot storage.

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In those studies, convenience yield is separated from storage cost. However, in the present study, we include the storage cost in the convenience yield. Therefore, we will be analyzing the “net convenience yield.”

For example, see Mas-Colell et al. (1995).

See Duffie (2001).

In this paper, \({\mathbf {R}}_+\) is \(\{ x | x \ge 0 \}\) and \({\mathbf {R}}_+^N\) is\(\{ (x_n)_{n=1,\ldots ,N} | x_n \ge 0 \}\).

Here we assume that there is a risk-neutral probability; the firm’s expected discounted value of profits is defined under this probability. Although we modeled firm as a risk-neutral agent under the risk-neutral probability, even if we modeled firm as a risk-neutral agent under natural probability the consequence is the same by the linearity of expectation.

Note that the Gibson and Schwartz model is an example of the Miltersen and Schwartz model.

A convex function f is essentially smooth for \(C=int(dom f)\) if C is not empty, f is differentiable throughout C, and \(\lim _{n\rightarrow \infty } ||\nabla f(x_n)|| = + \infty \) whenever \(x_1, x_2, \cdots ,\) is a sequence in C converging to a boundary point x of C.

The author would like to thank the anonymous referee for the suggestion of this example in the preliminary draft.

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Titel: Commodity Spot and Futures Prices Under Supply, Demand, and Financial Trading: Single Input–Output Model
verfasst von: Katsushi Nakajima
Publikationsdatum: 08.08.2019
Verlag: Springer Japan
Erschienen in: Asia-Pacific Financial Markets / Ausgabe 1/2020
Print ISSN: 1387-2834
Elektronische ISSN: 1573-6946
DOI: https://doi.org/10.1007/s10690-019-09280-6

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