Mathematics of Financial Markets
This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophistica
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Editorial Board M. Avellaneda G. Barone-Adesi M. Broadie M.H.A. Davis E. Derman C. Klu¨ppelberg E. Kopp W. Schachermayer
Robert J. Elliott and P. Ekkehard Kopp
Mathematics of Financial Markets Second edition
Robert J. Elliott Haskayne School of Business University of Calgary Calgary, Alberta Canada T2N 1N4 [email protected]
P. Ekkehard Kopp Department of Mathematics University of Hull Hull HU6 7RX Yorkshire United Kingdom [email protected]
With 7 figures.
Library of Congress Cataloging-in-Publication Data Elliott, Robert J. (Robert James), 1940– Mathematics of financial markets / Robert J. Elliott and P. Ekkehard Kopp.—2nd ed. p. cm. — (Springer finance) Includes bibliographical references and index. ISBN 0-387-21292-2 1. Investments—Mathematics. 2. Stochastic analysis. 3. Options (Finance)—Mathematical models. 4. Securities—Prices—Mathematical models. I. Kopp, P. E., 1944– II. Title. III. Series. HG4515.3.E37 2004 332.6′01′51—dc22 2004052557 ISBN 0-387-21292-2
Printed on acid-free paper.
© 2005 Springer Science+Business Media Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com
(EB)
SPIN 10936511
Preface This work is aimed at an audience with a sound mathematical background wishing to learn about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and probability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or ‘exotic’) financial instruments that now appear on the derivatives markets; the focus throughout remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to financial markets. The first five chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by non-arbitrage) is presented in Chapter 1. The unique price for a European option in a single-period binomial model is given and then exte
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