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Equilibrium pricing of commodity spot and forward under incomplete markets with implications on convenience yield

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  • Katsushi Nakajima

    (Ritsumeikan Asia Pacific University)

Abstract

This paper analyzes the relation between commodity spot, forward prices, and convenience yield under incomplete markets. Since production is a necessary process for commodity markets, we include firms that use inputs and produce outputs in our model. Thus, we show a financial pricing model of spot and forward commodity in an explicit fashion with production under incomplete markets. One of the most important results of this paper is the difference between commodity spot and forward equilibrium price can be explained by the discounted shadow price of storage constraint minus the discounted marginal storage cost and it can be interpreted as the net convenience yield in the existing literature. Here the discounted factor is affected by the incompleteness of the markets. We prove the generic existence of the equilibrium and thus the obtained spot forward price relation is the equilibrium price formula. We also derive the firm’s optimal production plan and trading strategy.

Suggested Citation

  • Katsushi Nakajima, 2022. "Equilibrium pricing of commodity spot and forward under incomplete markets with implications on convenience yield," Annals of Finance, Springer, vol. 18(1), pages 35-80, March.
    • Handle: RePEc:kap:annfin:v:18:y:2022:i:1:d:10.1007_s10436-021-00402-7
    DOI: 10.1007/s10436-021-00402-7
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    More about this item

    Keywords

    Convenience yield; Differential topology; Forward price; General equilibrium; Incomplete market;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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