Stochastic Differential Equation Modelling of Asset Price Dynamics on the Nigerian Stock Exchange

Asset price dynamics on the Nigerian Stock Exchange exhibit stylised statistical properties including volatility clustering, heavy tails, and mean reversion that depart significantly from the assumptions of classical geometric Brownian motion models. This study employs a family of stochastic differential equation models, including geometric Brownian motion, the Heston stochastic volatility model, and the jump-diffusion model of Merton, to characterise daily return dynamics for 30 NSE-listed equities across five sectoral categories over the period 2018 to 2023. Model parameters are estimated using quasi-maximum likelihood and particle filter methods applied to high-frequency intraday data. Model adequacy is evaluated through statistical tests for residual autocorrelation, conditional heteroscedasticity, and departure from normality. The Heston model with correlated volatility process achieves the superior goodness-of-fit across all five sectors, confirming that stochastic volatility is a dominant feature of NSE price dynamics. Jump-diffusion models significantly outperform geometric Brownian motion in capturing extreme return events, particularly for the banking and oil and gas sectors. Option pricing implications of the estimated models are explored through Monte Carlo simulation of European option values, revealing meaningful mispricing in hypothetical options priced under geometric Brownian motion assumptions. Keywords: stochastic differential equations, asset pricing, Nigerian Stock Exchange, Heston model, jump-diffusion.