Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of asset returns is normal or lognormal. However, many empirical studies have revealed that return distributions are usually not normal. These studies, time and again, discover evidence of non-normality, such as heavy tails and excess kurtosis.Research purpose: This work was aimed at analysing the GBM with a sequential Monte Carlo (SMC) technique based on t-distribution and compares the distribution with normal distribution.Motivation for the study: The SMC or particle filter based on the t-distribution for the GBM model, which involves randomness, volatility and drift, can precisely capture the aforementioned statistical characteristics of return distributions and can predict the random changes or fluctuation in stock prices.Research approach/design and method: The particle filter based on the t-distribution is developed to estimate the random effects and parameters for the extended model; the mean absolute percentage error (MAPE) were calculated to compare distribution fit. Distribution performance was assessed through simulation study and real data. Main findings:Results show that the GBM model based on student's t-distribution is empirically more successful than the normal distribution. Practical/managerial implications:The proposed model which is heavier tailed than the normal does not only provide an approximate solution to non-normal estimation problem. Contribution/value-add:The GBM model based on student's t-distribution establishes an efficient structure for GBM and volatility modelling.

With energy serious shortage of the Nigerian Power Sector owing to industry deregulation, abrupt variations in electricity demand, and increasing population density, Nigeria's economic development has been restricted. Thus, it is significant to balance the relationship between power generation and consumption, and further stabilize the two in a reasonable scope. To achieve balance, an accurate model to fit and predict electricity generation and consumption in Nigeria is required. This study, therefore, proposes a comparative study on stochastic modeling; (Harvey model, Autoregressive model, and Markov chain model) for forecasting electricity generation and consumption in Nigeria. The data gathered were analyzed and the model parameters were estimated using the maximum likelihood estimation technique. The comparative performance revealed that the Markov chain model best-predicted electricity generation than the Harvey and Autoregressive models. Also, for electricity consumption, results showed that the Harvey model predicted best than the Markov and Autoregressive models for electricity consumption. Thus, the Markov and Harvey model used to forecast electricity generation and consumption in Nigeria for the next 20 years (2018 to 2037) did not only reveal that electricity generation and consumption will continue to increase from 3,692.11 mln kW/h to 18,250.67 mln kW/h and from 2,961.10 mln kW/h to 127,071.30 mln kW/h respectively but also indicates high accuracy and the reference value of these models.