Estimating and pricing commodity futures with time‐delay stochastic processes

Abstract

In commodity futures pricing models, the commodity present price is gener-ally considered to reflect all information in the markets and past information isnot regarded important. However, there is some empirical evidence that showsthat this fact is unrealistic. In this paper, we consider some stochastic mod-els with delay for pricing commodity futures. The functions of the commodityprice stochastic process under the risk-neutral measure are necessary for pricingderivatives. However, the observations in the market have risk. Then, we use atechnique that allows us to estimate the functions of the risk-neutral commodityspot price stochastic process, directly from futures prices traded in the market,and show how to price the commodity futures. Finally, we make an empiricalapplication of this methodology with gold futures traded in the COMEX. Fur-thermore, we make clear the supremacy of the delay models in pricing goldfutures.