This thesis has outlined several fundamental concepts underlying option theory. It consists of four main parts: asset price dynamics, pricing models for plain vanilla options, sensitivities and implied volatilities. There are undoubtedly numerous books explaining these concepts, the logic behind and the mathematics. However, the objective of this thesis has been to focus on the subject of incorporating computational tools within option theory.
It is therefore an interactive tutorial, which offers the reader not only computational examples, but more importantly, the possibility to directly switch to XploRe . The reader is then able to substantiate theoretical results asserted in the thesis, or alternatively is able to apply XploRe in order to pose questions and receive satisfactory answers. By using graphical tools within XploRe for sensitivities and volatility surfaces, it is then possible for the reader to obtain a feeling for the impact of different factors, especially volatility, on the option price.
This thesis has taken for granted the fact that the reader has prior knowledge on options and therefore does not address several basic but important questions, for example: 'why do options exists', 'what gives them value' and 'how are these products used for trading and hedging'? It also does not cover extensions of the classical Black-Scholes model to incorporate such features as stochastic volatility, or extensions to higher dimensionality for options on more than one underlying asset. It neither discusses exotic options, although there is an awareness of their recent expansion in trading, or current pricing theory that is based on martingale methods, which adopt a unified approach to all forms of derivatives, options included. Nevertheless, it covers the basics of option evaluation, introduced in the equity world, including numerous examples from XploRe .