Commodity Price Modeling by Optimal Storage Time

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. 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. Finally, we conduct some sensitivity analysis to show the impact of the parameters on SREE