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  .
In commodity markets, the convergence of futures towards spot prices as the time to maturity of the contracts goes to zero is usually justified by no-arbitrage arguments. In this paper 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 commodity: it remains suitable for commodities characterized by storability constraints, when standard no-arbitrage arguments can not be safely applied .
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