A JUMP DIFFUSION PROCESS MODELLING OF NIGERIAN BONNY LIGHT CRUDE OIL PRICES

Abstract

Many attempts have been made to study and model the dynamics of the Nigeria crude oil production but not many recent works in the literature have employed stochastic differential equations in modelling crude oil prices like financial derivatives. Oil differs from financial assets in that futures prices are often below spot prices, and the degree of backwardness is highly variable over time. Oil prices are volatile and deviates from the assumptions made in many commodity pricing models which is the assumption of Gaussian dynamics for the spot price. From the foregoing, this study sought to further examine the stochastic volatility present in monthly Nigeria Bonny light crude oil prices and extend the Merton jump diffusion (MJD) model to capture the discontinuities in the trajectories of the prices as a jump process, while capturing statistical features present in the historical time series such as seasonality, mean reversion and dependencies among spot prices. Our approach involved modelling the Poisson intensity in the Levy process as exponentially decaying function. Our approach was compared with Gaussian diffusion processes of geometric Gaussian motion, Ornstein-Uhlenbeck stochastic process and its extension with mean reverting property as well as with MJD process. Simulations and application to Nigeria’s Bonny light crude oil prices were used to compare the performances of the models. The MJD and our approach were very close in their parameters estimates as against the Gaussian diffusion processes and were preferred to them as evidenced by the AIC, BIC and log-likelihood. For the crude oil price modelling, the comparisons also favoured our approach over MJD process.