Title: On a new model for commodity price by optimal storage time and application in pricing options
Abstract: We propose a modified version of the speculative storage model of Deaton and Laroque (1992) in a continuous-time framework. Unlike most of the literature, where either the demand or the price process are exogenously given, our framework models them endogenously for the storable commodities. This shows that how the commodities’ economic characteristics like the demand elasticity and stylized facts like the price volatility can specify the prices. In addition, our model gives rise to the concept of the storage option and the optimal selling time. Using techniques from PDE theory and also stochastic analysis, we prove the existence, and under very mild conditions, the uniqueness of the stationary rational expectations equilibrium (SREE), and introduce practical ways to approximate it. We also derive the PDEs for the pricing of the options and see how the economic factors will impact the price of the options.