Brandimarte - Numerical Methods in Finance and Economics 20: A MATLAB-Based Introduction

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Library of Congress Cataloging-in-Publication Data:

Brandimarte, Paolo.

Numerical methods in finance and economics : a MATLAB-based introduction / Paolo

Brandimarte.2nd ed.

p. cm.

Rev. ed. of: Numerical methods in finance. 2002.

Includes bibliographical references and index.

ISBN-13: 978-0-471-74503-7 (cloth)

ISBN-10: 0-471-74503-0 (cloth)

1. FinanceStatistical methods. 2. EconomicsStatistical methods. I. Brandimarte, Paolo.

Numerical methods in finance. II. Title.

HG176.5.B73 2006

332.0151dc22

2006045787

10 9 8 7 6 5 4 3 2 1

This book is dedicated to Commander Straker, Lieutenant Ellis, and all SHADO operatives. Thirty-five years ago they introduced me to the art of using both computers and gut feelings to make decisions.

Preface to the Second Edition

After the publication of the first edition of the book, about five years ago, I have received a fair number of messages from readers, both students and practitioners, around the world. The recurring keyword, and the most important thing to me, was useful. The book had, and has, no ambition of being a very advanced research book. The basic motivation behind this second edition is the same behind the first one: providing the newcomer with an easy, but solid, entry point to computational finance, without too much sophisticated mathematics and avoiding the burden of difficult C++ code, also covering relatively non-standard optimization topics such as stochastic and integer programming. See also the excerpt from the preface to the first edition. However, there are a few new things here:

• a slightly revised title;
• completely revised organization of chapters;
• significantly increased number of pages.

The title mentions both Finance and Economics, rather than just Finance. To avoid any misunderstanding, it should be made quite clear that this is essentially a book for students and practitioners working in Finance. Nevertheless, it can be useful to Ph.D. students in Economics as well, as a complement to more specific and advanced textbooks. In the last four years, I have been giving a course on numerical methods within a Ph.D. program in Economics, and I typically use other available excellent textbooks covering advanced algorithms which can be used to solve a wide array of problems in Economics. From the point of view of my students in such a course, the present book has many deficiencies: For instance, it does not cover ordinary differential equations and it does not deal with computing equilibria or rational expectations models; furthermore, practically all of the examples deal with option pricing or portfolio management. Nevertheless, given my experience, I believe that they can benefit from a more detailed and elementary treatment of the basics, supported by simple examples. Moreover, I believe that students in Economics should also get at least acquainted with topics from Operations Research, such as stochastic programming and integer programming. Hence, the and Economics part of the title suggests potential use of the book as a complement, and by no means as a substitute.

The book has been reorganized in order to ease its use within standard courses on numerical methods for financial engineering. In the first edition, optimization applications were dealt with extensively, in chapters preceding those related to option pricing. This was a result of my personal background, which is mainly Computer Science and Operations Research, but it did not fit very well with the common use of a book on computational finance. In the present edition, advanced optimization applications are left to the last chapters, so they do not get into the way of most financial engineering students. The book consists of twelve chapters and three appendices.