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Option Theory with Stochastic Analysis

An Introduction to Mathematical Finance

  • Textbook
  • © 2004

Overview

Authors:
  1. Fred Espen Benth

    1. Department of Mathematics, Centre of Mathematics for Applications University of Oslo, Oslo, Norway

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  • Very concise, requires only basic mathematical skills
  • Describes the basic assumptions (empirical finance) underlying option theory
  • Includes a big section on pricing using both pde-approach and martingale approach (stochastic finance)
  • Presents the two main approaches for numerical computation of option prices (computational finance)
  • Can be used at introductory level at universities, with exercises after each chapter
  • Potential interest for the German actuaries and actuarial training

Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Introduction

    • Fred Espen Benth
    Pages 1-10

  3. Statistical Analysis of Data from the Stock Market

    • Fred Espen Benth
    Pages 11-32

  4. An Introduction to Stochastic Analysis

    • Fred Espen Benth
    Pages 33-52

  5. Pricing and Hedging of Contingent Claims

    • Fred Espen Benth
    Pages 53-97

  6. Numerical Pricing and Hedging of Contingent Claims

    • Fred Espen Benth
    Pages 99-119

  7. Back Matter

    Pages 121-166
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Keywords

About this book

Since 1972 and the appearance of the famous Black & Scholes option pric­ ing formula, derivatives have become an integrated part of everyday life in the financial industry. Options and derivatives are tools to control risk ex­ posure, and used in the strategies of investors speculating in markets like fixed-income, stocks, currencies, commodities and energy. A combination of mathematical and economical reasoning is used to find the price of a derivatives contract. This book gives an introduction to the theory of mathematical finance, which is the modern approach to analyse options and derivatives. Roughly speaking, we can divide mathematical fi­ nance into three main directions. In stochastic finance the purpose is to use economic theory with stochastic analysis to derive fair prices for options and derivatives. The results are based on stochastic modelling of financial as­ sets, which is the field of empirical finance. Numerical approaches for finding prices of options are studied in computational finance. All three directions are presented in this book. Algorithms and code for Visual Basic functions are included in the numerical chapter to inspire the reader to test out the theory in practice. The objective of the book is not to give a complete account of option theory, but rather relax the mathematical rigour to focus on the ideas and techniques.

Reviews

From the reviews:

"This is a … book concerned solely with describing the mathematics of option pricing and I found it a delight to read. It is very well written, quite comprehensive and non-rigorous so that it can be used on courses aimed at a variety of students. … The book includes a healthy number of exercises and there are fully worked solutions to most of these." (David Applebaum, The Mathematical Gazette, Vol. 90 (517), 2006)

"The book provides an introduction to the basic ideas of the mathematical theory of financial options valuation, or, more concretely, to the Black-Scholes theory of pricing contingent claims on equity. … The text is a brief, neat, carefully written introduction to the fundamentals of the mathematics and the modelling of the analysis of options pricing." (José Lúis Fernandez Perez, Zentralblatt MATH, Vol. 1042 (17), 2004)

Authors and Affiliations

  • Department of Mathematics, Centre of Mathematics for Applications University of Oslo, Oslo, Norway

    Fred Espen Benth

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