International Journals of Marketing and Technology
  • Year: 2012
  • Volume: 2
  • Issue: 1

Estimation of market volatility-A case of logistic brownian motion

  • Author:
  • D. B. Oduor1, N. Omolo Ongati2, N. B. Okelo2, Silas N. Onyango3
  • Total Page Count: 12
  • Page Number: 37 to 48

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.

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.

Keywords

Volatility, Modeling, Brownian motion, differential equation, Dupire's equation