Estimating and pricing commodity futures with time‐delay stochastic processes

Abstract

In commodity futures pricing models, the commodity present price is generally considered to reflect all information in the markets and past information is not regarded important. However, there is some empirical evidence that shows that this fact is unrealistic. In this paper, we consider some stochastic models with delay for pricing commodity futures. The functions of the commodity price stochastic process under the risk‐neutral measure are necessary for pricing derivatives. However, the observations in the market have risk. Then, we use a technique that allows us to estimate the functions of the risk‐neutral commodity spot price stochastic process, directly from futures prices traded in the market, and show how to price the commodity futures. Finally, we make an empirical application of this methodology with gold futures traded in the COMEX. Furthermore, we make clear the supremacy of the delay models in pricing gold futures.