A Note on the Spot-Forward No-Arbitrage Relations in an Investment-Production Model for Commodities



René Aïd, Luciano Campi, Delphine Lautier

Because of storability constraints, standard no-arbitrage arguments cannot be safely applied in markets of commodities such as energy. In this paper, we propose an alternative approach to justify the convergence of forward towards spot prices as time-to-maturity goes to zero. We show that the classical no-arbitrage relationship between spot and forward prices holds through the well-posedness of an expected profit maximization problem for an agent producing and storing a commodity while trading in forward contracts. A consequence of this is that the forward price of energy can be seen as risk-neutral expectation of the spot price at maturity. Moreover, we obtain an explicit formula for the forward volatility and provide a heuristic analysis of the optimal solution for the production/storage/investment problem in a Markovian setting.

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