Black and Scholes  approach to option price estimations and option trading brought about a great breakthrough in financial mathematics. Since Black and Scholes , the standard model in financial mathematics has been the Geometric Brownian motion. In this model it is assumed that the asset’s log return has a normal distribution with volatility and drift terms. The model has proved to have very attractive features. However, from empirical study, geometrical Brownian motion cannot accurately reflect all behaviors of the stock quotation. The model has some limitations in price prediction, especially when used to model the price over short period of time. The study involves derivation of logistic Brownian motion with jump diffusion for a better study of the behavior of the underlying asset.
Andanje Mulambula "Logistic Brownian Motion with Jumps" Iconic Research And Engineering Journals Volume 5 Issue 3 2021 Page 98-101
Andanje Mulambula "Logistic Brownian Motion with Jumps" Iconic Research And Engineering Journals, 5(3)