Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Davison, Matthew


A commodity market participant trading via her inventory has access to both spot and forward markets. To liquidate her inventory, she can sell at the spot price, take a short forward position, or do a combination of both. A trade is proposed in which there is always a hedging forward contract, which can be considered a dynamic cash and carry arbitrage. The trader can adjust the maturity of the forward contract dynamically until the inventory is depleted or a time constraint is reached. In the first setup, the storage contract (to carry inventory) is assumed to have a constant cost and a flexible duration. The risk and return characteristics of an Approximate Dynamic Programming (ADP) and a Forward Dynamic Optimization solution are compared. The trade is contrasted with optimal spot sale among other alternative liquidation strategies. Independent from the underlying stochastic forward price model, it is proved and verified numerically that a partial sale strategy is not optimal. The optimally selected forward maturities are limited to the subset comprising the immediate, next, and last timesteps. Under a more realistic storage contract, which assumes a stochastic cost and a fixed duration, a new ADP approach is developed. The optimal policy shows the tanker rent decision is accompanied by a buy order since the loss from an empty tanker is more than the gain of renting it cheaply yet early. Given the nonadjustable duration of the rent contract, a longer contract generates a higher value by benefiting from a tanker refill option.