Abstract: Modelling the stochastic behaviour of stock prices have been an exciting challenge for applied statisticians and mathematical economists. Statistical models have commonly been used in the analysis and forecasting of time series data. Usually, the best model is selected to forecast future outcomes based on a selection criterion. This study investigates the longitudinal pattern of Nigerian insurance stock option prices. The present study considers the Expert Model Mining System (EMMS), which incorporates a set of competing methods such as Exponential Smoothing (ES), Auto Regressive Integrated Moving Average (ARIMA) and seasonal ARIMA models. The selection process uses the Bayesian Information Criterion (BIC). However, the Mean Square Error (MSE) and the Coefficient of Determination (R²) statistics are also being included in probing the adequacy of the selected model. Empirical analysis results show that most stock option prices portrayed exponential smoothing growth behaviour. In fact, all the simulated models are quite good with a minimal coefficient of determination of 97%. Moreover, despite the direct capital and premium incomes triggered by the free market consolidation exercises and the growth portrayed by the stock prices, the insurance industry is still very much undercapitalize with market capitalization of only 5% of Nigerian Stock Exchange (NSE). Finally, the situation is quite alarming, when comparing Nigerian insurance density and market penetration to others major African countries.