A Bimodal Model for Oil Prices

Joanna Goard () and Mohammed AbaOud
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Joanna Goard: School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia
Mohammed AbaOud: Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Mathematics, 2023, vol. 11, issue 10, 1-26

Abstract: Oil price behaviour over the last 10 years has shown to be bimodal in character, displaying a strong tendency to congregate around one range of high oil prices and one range of low prices, indicating two distinct peaks in its frequency distribution. In this paper, we propose a new, single nonlinear stochastic process to model the bimodal behaviour, namely, d p = α ( p 1 − p ) ( p 2 − p ( p 3 − p ) d t + σ p γ d Z , γ = 0 , 0.5 . Further, we find analytic approximations of oil price futures under this model in the cases where the stable fixed points of the corresponding deterministic model are (a) evenly spaced about the unstable fixed point and (b) are spaced in the ratio 1:2 about the unstable fixed point. The solutions are shown to produce accurate prices when compared to numerical solutions.

Keywords: futures on oil valuation; analytical approximations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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