TITLE:
A Mathematical Formulation of the Valuation of Brent Oil Futures Contracts
AUTHORS:
Rebecca Abraham
KEYWORDS:
Brent Crude Oil Futures, Commodity Pricing, Geopolitical Risk, Oil Price Prediction, Mathematical Models
JOURNAL NAME:
Theoretical Economics Letters,
Vol.16 No.5,
September
30,
2026
ABSTRACT: Oil is a commodity. The inelastic demand for gasoline to power electrical grids in homes and buildings, and power automobiles results in the need to examine oil prices. Oil futures trade on commodity exchanges, such as the Chicago Mercantile Exchange in the United States. Oil prices consist of a spot price (current price) and a speculative price. The purpose of this paper is to create mathematical models that describe optimal oil prices as a function of investor sentiment and oil price fluctuations. Three types of investors are examined. Risk-averse investors adopt a gamma distribution with decreasing propensity to purchase oil futures with increasing speculative price fluctuations. Moderate risk-takers assume a Bessel function with revisions of price forecasts as new information becomes available. Risk-takers’ sentiments are modeled by an exponential distribution as they seek higher oil price returns with increasing risk. Oil price speculation is modeled by a Levy jump process, as oil prices follow jump discontinuities as past prices may not be linked to future prices during periods of high geopolitical risk, such as the US-Iran war in the Middle East. The mathematical models are empirically validated using contemporary price-volume data on Brent oil futures prices. Empirical findings support the mathematical conjecture of differential price expectations of the three types of investors, and their influence on final prices. Applications of the models developed in this paper to other commodities, such as gold and silver, are discussed.