1Department of Mathematics and Applied Statistics, Maseno University, P.O Box-333, Maseno – Kenya
2School of Mathematics and Actuarial Science, Bondo University College, Box 210 – 406001, Bondo – Kenya
3Faculty of Commerce and Distance Learning, KCA University, P.O Box-56808, Nairobi – Kenya
Online published on 29 June, 2013.
In this paper, we have used the Dupire's equation to derive the volatility model when the asset price follows logistic Brownian motion. We have used the analysis of Brownian motion, logistic Brownian motion, derivation of Black-Scholes Merton differential equation using It^o process and It^o's lemma and stochastic processes. We have also reviewed derivation of Dupire Volatility equation and used it's concept to derive a volatility model when the asset price follows logistic Brownian motion.
Volatility, Modeling, Brownian motion, differential equation, Dupire's equation
