Optimal dynamic commodity liquidation by joint spot and forward contracts

This paper studies the problem of optimal liquidation of an inventory through spot and forward markets over a finite time horizon. The decision maker can sell her inventory on the spot market or take a short position in a forward contract or both. At every time step, the maturity of the forward contract can be adjusted until the inventory is completely depleted. Considering this forward contract whose maturity can be dynamically updated, in addition to liquidation in the spot market, is one of the salient characteristics of our problem in this paper. We formulate this problem as a stochastic dynamic optimization problem, and prove that a ‘partial sale’, i.e. dividing the sale between the spot and forward market, is not optimal, regardless of the underlying price model. Next, we show that the optimally selected forward maturity is limited to the immediate, next, or last timestep, under certain linearity assumptions. This result can significantly reduce the computational complexity of the dynamic optimization model, by considerably reducing the search space. Next, we develop an Approximate Dynamic Programming approach to compute an adaptive liquidation policy. The performance of the proposed solution method is numerically assessed and compared against the exact policy and other alternative policies, in terms of both achieved return and risk attributes.