Multivariate Time-Changed Brownian Motion

Abstract

The main topics covered in this chapter are:the history of time-changed Brownian motion and why this process has been applied to finance;the main properties and formulas for different parametric examples of multivariate time-changed Brownian motion;the relation between multivariate time-changed Brownian motion and multivariate normal mean–variance mixture distributions;the derivation of the closed formula for the density function of some multivariate normal mean–variance mixture laws;the evaluation of the probability density function of a multivariate normal mean–variance mixture law when only the characteristic function of the mixing distribution is available in closed form while the density function is not;how to generate sample draws from a multivariate normal mean–variance mixture law.