# Generalized Random Walks, Their Trees, and the Transformation Method of Option Pricing Generalized Random Walks, Their Trees, and the Transformation Method of Option Pricing

Several properties of the generalized random walk are considered. First, the limiting distribution of the generalized random walk is shown to include a large class of distributions. Second and in conjunction with the first, the generalized random walk is compared to the geometric random walk. It is shown that when parametrized properly, the generalized random walk does converge to the lognormal distribution. Third, and perhaps most interesting, is one of the limiting properties of the generalized random walk. In the limit, generalized random walks are closely connected with a u function. The u function is the key link between generalized random walks and its difference equation. Last, we apply the generalized random walk to option pricing.

Advisor:

School:Brigham Young University

School Location:USA - Utah

Source Type:Master's Thesis

Keywords:generalized random walk binomial tree asset pricing model

ISBN:

Date of Publication:08/12/2008