Simulating stock prices using geometric Brownian motion model under normal and convoluted distributional assumptions

Abstract

This study proposes a modified Geometric Brownian motion (GBM), to simulate stock price paths under normal and convoluted distributional assumptions. This study utilised four selected continuous probability distributions for the convolution because of shared properties, including normality, and parameters that have a standard distribution with a location and scale parameters of zero and one, in that order. The findings from this study revealed that the simulation of price paths looks identical under the assumption of normal distribution and normal convolved with normal, Laplace, and Rice distributions for different sample sizes and parameter settings but differs with respect to the Cauchy distribution. Furthermore, the study found that all the mean absolute percentage error (MAPE) and mean square error (MSE) values for the normal and convoluted distributions underlying the GBM were approximately less than 10%, indicating high forecast accuracy. However, the average simulated price paths for the GBM under the normal distribution was found to be significantly different from the GBM under convoluted distribution when a t-test was employed for different sample sizes and different settings of the drift and volatility values.