This study considers a business scenario involving three participants. The first participant, in this case the farmer sells the cattle to the second participant, in this case the Botswana Meat Commission (BMC) which, in turn sells the processed beef to the European Union (EU). The BMC offers a price, S1(t), to the farmer for the cattle. The EU offers a price, S2(t), to the BMC. To estimate the parameters spot prices of beef-cattle from the BMC and the EU markets for years 1992 to 2018 were used. This study considers the relationship between S1(t) and S2(t), how the two prices are correlated and whether there is any seasonal dependence on the prices. First, we constructed a bivariate model which showed strong correlation between the prices S1(t) and S2(t) and that the residue between S1(t) and S2(t) is explained by a white noise process. Based on this result, we constructed a stochastic model for the farmer price, S1(t), of the Ornstein-Uhlenbeck type where the EU price is assumed as the mean. Several scenarios arose from the stochastic model covering a number of possibilities ranging from collapse of the business for the farmer to thriving business with mean reverting returns. The study gives insight why the BMC which is caught in between the farmer and the EU is experiencing operational problems financially.

Thesis (MSc of Science in Pure and Applied Mathematics)---Botswana International University of Science and Technology, 2021