*Department of Mathematics and Applied Statistics, Maseno University, P.O Box 333, Maseno - Kenya
**Faculty of Commerce and Distance Learning, KCA University, P.O Box 56808, Nairobi, Kenya
Online published on 26 September, 2013.
In this paper, we have used the idea of Onyango (2003) he used to develop a logistic equation used in natural science to develop a logistic geometric Brownian motion with a price of dividend yielding asset since in reality, assets do pay dividends to shareholders at regular intervals after a maturity period which normally after one year. We have first derived a deterministic Walrasian price-adjustment model with price of dividend yielding asset after which we have introduced the stochastic effect of noise to derive a logistic geometric Brownian motion with a unique volatility function σ(S,t) such that the observed option price is consistent with the price of the dividend yielding asset model.
Volatility, Modeling, Geometric Brownian motion, Supply and Demand functions, Equilibrium price, Walrasian excess demand function, deterministic Walrasian price-adjustment model, Logistic Brownian motion
