Research on Geometric Brownian motion and its practice in pricing

In this paper a stochastic calculus is given for the fractional Brownian motions that have the Hurst parameter in (1/2, 1). A stochastic integral of Itô type is defined for a family of integrands so that the integral has zero mean and an explicit ...

Fractal Brownian motion, also called fractional Brownian motion fBm, is a class of stochastic processes characterized by a single parameter called the Hurst parameter, which is a real number between zero and one. fBm becomes ordinary standard Brownian ...

The paper presents the construction and simulation of n-dimensional Brownian motion, a continuous-time stochastic process, and an important stochastic model: the Black-Scholes model. This model is deriving from partial differential equation and solved ...