The Role of Expectations in Commodity Futures Markets

根据不同商品的性质、特点和交易习惯，存在着多种多样的商品期货市场。因此，我想构建一个现实的，以及一般的模型。为了明确地阐明预期的作用，我将商品期货市场的参与主体按其功能分为(1)套期保值者，(2)投机者，(3)未套期保值库存持有者，(4)消费者。接下来，我制定了前两个实体的商品期货需求和供应时间表。此外，我试图以相当简单的函数形式制定未对冲的库存和消费表。我在制定这些表时，除了消费表外，都尽量强调预期的作用，因为它们一般都取决于未来现金和期货价格的期望值，或者是未来现金价格与当前期货价格的差值。我用线性近似来表示它们，因为我的主要目的是求解模型。此外，通过对期货和库存市场施加两个均衡条件，得到了给定价格预期下均衡期货和现金价格的半约简形式。显然，在这种简化模型中，外生变量的半约简形式的系数的符号不能在某些严格的假设下确定。在某种程度上，在更严格的假设下，预期对需求和供给的影响的路径和方向是明确的。很明显，由于现金和期货价格基本上都是在动态模型中确定的，未来可能有必要在动态环境中重新制定模型，在这种情况下，假设效用函数的优化将是一个合适的分析框架。

There exist a variety of commodity futures markets depending on the natures, characteristics, and the transaction customs of individual commodity. Thus, I would like to construct a a realistic, as well as a general model. In order to elucidate the role of expectations explicitly, I classified the participating entities in the commodity futures markets by their functions into (1)hedgers, (2)speculators, (3)holders of unhedged inventories, and (4)consumners. Next, I formulated the demand and the supply schedules of commodity futures by the former two entities. Furthermore, I tried to formulate unhedged inventories and consumption schedules in rather simple functional forms. I tried to formulate these schedules, except the consumption one, to emphasize the role of expectations, because they in general depend on the expected values of cash and futures prices in future, or the difference between the expected future cash price and the current futures price. I formulated them by linear approximation, because my primary purpose is to solve the model. Furthermore, by imposing two equilibriun conditions for the market for futures and inventories, I derived the the semi-reduced forms of equilibrium futures and cash prices under given price expectations. It was made clear that, within such a simplified model, the signs of coefficient of exogenous variables in the semi-reduced forms cannot be determined under some stringent assumptions. The route and the direction of the effects of expectations on the demand and the supply were, to some extent, made clear under still more stringent assumptions.It was made clear that, because both the cash and the futures prices are determined basically in a dynamic model, it may be necessary in the future to reformulate the model in a dynamic setting, and in that case, an optimization of an assumed utility function will be an appropriate analytical framework.