On the spot-futures no-arbitrage relations in commodity markets

TL;DR

This paper introduces an alternative framework based on profit maximization for understanding the relationship between spot and futures prices in commodity markets, especially useful for energy commodities with storage constraints.

Contribution

It presents a novel approach linking futures-spot relations to an agent’s optimization problem, extending no-arbitrage concepts to storability-constrained commodities.

Findings

Futures price equals the risk-neutral expectation of the spot price.

Provides an explicit formula for forward volatility.

Offers heuristic analysis of optimal production, storage, and trading strategies.

Abstract

In commodity markets the convergence of futures towards spot prices, at the expiration of the contract, is usually justified by no-arbitrage arguments. In this article, we propose an alternative approach that relies on the expected profit maximization problem of an agent, producing and storing a commodity while trading in the associated futures contracts. In this framework, the relation between the spot and the futures prices holds through the well-posedness of the maximization problem. We show that the futures price can still be seen as the risk-neutral expectation of the spot price at maturity and we propose an explicit formula for the forward volatility. Moreover, we provide an heuristic analysis of the optimal solution for the production/storage/trading problem, in a Markovian setting. This approach is particularly interesting in the case of energy commodities, like electricity: this framework indeed remains suitable for commodities characterized by storability constraints, when standard no-arbitrage arguments cannot be safely applied.