BT METHODS AND OPTION PRICING

Binomial Tree Methods and Option Pricing



A Report developed and presented in the Department of Mathematics, Statistics and Engineering Science, Coventry University, for the Degree of Bachelor of Science in Financial Mathematics April 2011

Acknowledgement

Great appreciation to my supervisor Christian Von Ferber for his support and research tips and material that has helped a great deal towards this project. Also many thanks to the author of the book “Option futures and other derivatives”, John C. Hull, for its financial inspirational theories and methods. Some chapters in this book has outlined the format of this project and contributed to the overall structure and information within the report, and many thanks to Keith Redhead (one of Coventry University's finance lecturers) for presenting information from a book that he has published. Furthermore a special thank you to the employers of the companies of PWC and J.P. Morgan for their insights and contribution to my research of particular topics on this project.

Abstract

This paper attempts to deal with, in a non-technical way, the basic assumptions underlying option pricing theory and point out some of the natural weaknesses they involve in the reliability of the resulting valuations. This paper presents a number of concrete examples to show that the impact of the modelling assumptions and selecting input parameters for the models. This project points out the importance for anybody involved in the finance world, to be aware of such many issues and persuade them to gain at least a superficial understanding of the quantitative aspects of an option pricing.

This concept of option pricing is to be used to build up a different model to price the items that have a fixed date to expiry. A financial model which is a binomial option pricing model which is implemented, to show that the option towards cut value, contributes in a positive way to a company's expected profitability, such as the pricing of airline seats or hotel rooms is used to express the approach of this options model.

The assumption in the Black-Scholes model is that the price of stock is at all times log normally distributed (so the price follows a concept of the Wiener process with constant variance). This option pricing model has been put to extensive, thorough and systematic use for both in research and in actual market place. However, the information and inputs for the models are generally gained from the stock market which is thought to have a lack of information and is thought to be less efficient than the options market. This generally leads to a difference in a calculated price and an observed price.

The Black Scholes models and the binomial tree model are used to work out the value of the price of the vanilla American options and also the vanilla European options. This paper presents how option prices can be determined for an underlying asset with prices that follow a random walk in discrete steps and also studies the relationship between the binomial tree and the underlying random ...