文章 — University of Reading

In this we examine the concept of the dimension of fractals, extending the idea of integer dimension to fractals, which we define and investigate here in. Moving on we consider the Minkowski dimension, sometimes referred to as the "box dimension", of a fractal. We then continue to define and examine another type of dimension; the Hausdorff dimension. We then investigate under what conditions these are equal finally moving on to prove Hutchinsons Theorem,

In this paper we discuss how to price American, European and Asian options using a geometric Brownian motion model for stock price. We investigate the analytic solution for Black-Scholes differential equation for European options and consider numerical methods for approximating the price of other types of options. These numerical methods include Monte Carlo, binomial trees, trinomial trees and finite difference methods. We conclude our discussion with an investigation of how these methods perform with respect to the changes in different Greeks. Further analysing how the value of a certain Greeks affect the price of a given option.