Stochastic Modelling of Crude Oil Price Dynamics and Its Implications for Nigeria’s Fiscal Planning

This study develops stochastic models of crude oil price dynamics and analyses their implications for Nigeria's fiscal planning framework, addressing a fundamental source of macroeconomic uncertainty in an economy where oil revenues finance approximately half of federal government expenditure. The high volatility of global crude oil prices, driven by geopolitical events, demand shocks, and OPEC production decisions, creates significant revenue uncertainty that renders deterministic budget projections unreliable for fiscal management purposes. Daily Brent crude oil price data from January 2005 to December 2023 are analysed, with particular attention to the distributional properties of returns, volatility clustering, and jump behaviour. Geometric Brownian motion, mean-reverting Ornstein-Uhlenbeck processes, and jump-diffusion models incorporating Poisson-distributed price jumps are estimated and compared on statistical goodness-of-fit criteria. The Heston stochastic volatility model is fitted to oil price return data to capture the volatility surface implied by historical price behaviour. Estimated stochastic process parameters are used to simulate a large ensemble of crude oil price paths over a five-year horizon, from which probability distributions of Nigeria's oil revenue under the 2024 Medium-Term Expenditure Framework assumptions are derived. Results show that deterministic price assumptions in current fiscal planning significantly understate oil revenue risk, with a 25 percent probability that actual oil revenues will fall more than 30 percent below budget projections in any given year. Keywords: stochastic modelling, crude oil prices, geometric Brownian motion, fiscal planning, Nigeria