On the distribution of market volatility

Abstract

In the derivation of the celebrated Black-Scholes-Merton Option Price Model, volatility is assumed to be constant. Recent studies have shown that this is not always the case. Estimation of volatility has occupied most of the researchers' time and many estimation models have been developed. We introduce a moving-window method to find the distribution of market volatility. Further more, test results of simulations of Geometric Brownian Motions show that market volatility follows a chi-square inverse distribution.

Keywords: Market volatility, Geometric Brownian Motion, Chi-distribution, moving-window

> East African Journal of Statistics Vol. 1 (2) 2006: pp. 175-184