Optimal Dynamic Liquidation of an Inventory via Forward Markets

Abstract

In commodity markets, a trader selling her inventory over a finite time horizon has access not only to the spot market but also to forward contracts. The trader has the choice to sell at the spot price, or to short a forward contract for later delivery, or a combination of both. While the commodity is hedged with the forward contract and carried in the inventory, the trader can dynamically adjust the maturity of the forward contract at each time step until the inventory is completely depleted. This paper investigates the optimal liquidation strategy for such a trader in the above framework, which can be considered a dynamic extension of the cash and carry arbitrage that may arise in contango markets. It is proved, independent of the underlying stochastic forward price model, that a ‘partial sale’ strategy involving the sale of the inventory across different contracts is not optimal. In addition, under a linearity assumption on the forward price differences, the optimally selected forward maturity is limited to a subset comprising the immediate (spot), next, or last time stage. The theoretical results imply that the optimal actions set is considerably smaller than the feasible set. An Approximate Dynamic Programming (ADP) policy is developed, and compared to the solution achieved by an exact grid-based technique and a Forward Dynamic Optimization (FDO) approach. The risk and return characteristics of ADP and FDO methods are contrasted. The theoretical propositions are verified numerically, and found to reduce computational times significantly.