[Robert L. Navin] The Mathematics Of Derivatives

The Mathematics of Derivatives
Tools for Designing Numerical Algorithms

ROBERT L. NAVIN

John Wiley & Sons, Inc.

The Mathematics of Derivatives

Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronicproducts and services for our customers’ professional and personal knowledge and understanding. The Wiley Finance series contains books written specifically for finance and investment professionals as well as sophisticated individual investors and their financial advisors. Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation, and financialinstrument analysis, as well as much more. For a list of available titles, visit our Web site at www.WileyFinance.com.

The Mathematics of Derivatives
Tools for Designing Numerical Algorithms

ROBERT L. NAVIN

John Wiley & Sons, Inc.

Copyright c 2007 by Robert L. Navin. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No partof this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit ofLiability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representativesor written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our otherproducts and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our Website at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Navin, Robert L. The mathematics of derivatives: tools for designing numerical algorithms/Robert L. Navin. p. cm. –(Wiley finance series) Includes bibliographical references. ISBN-13: 978-0-470-04725-5 (cloth) ISBN-10: 0-470-04725-9 (cloth) 1. Derivative securitie–Valuation–Mathematical models. I. Title. II. Series.HG6024.A3N37 2007 332.64’57015181–dc22 2006017013 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

This book is dedicated with love to Thais Roda Noya.

Contents
Preface Acknowledgments PART I The Models xi xiii 1
3
3 3 3 5 6 7 8 10

CHAPTER 1 Introduction to the Techniques of Derivative Modeling
1.1 Introduction 1.2 Models 1.2.1 What Is a Derivative? 1.2.2 What Is a Model?...