Estimation of market volatility-A case of logistic brownian motion

Abstract

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.