Universitext Springer-Verlag Berlin Heidelberg GmbH Jürgen Franke· Wolfgang Härdle . Christian Hafner Statistics of Financial Markets An Introduction Springer Professor Dr. Jürgen Franke University of Kaiserslautern P.O. Box 3049 67653 Kaiserslautern Germany e-mail: [email protected] Professor Dr. Wolfgang Härdle Humboldt-Universität zu Berlin CASE-Center for Applied Statistics and Economics Spandauer Str. 1 10178 Berlin Germany e-mail: [email protected] Professor Dr. Christian M. Hafner Erasmus University Rotterdam Econometric Institute, Faculty of Economics P.O. Box 1738 3000 DR Rotterdam The Netherlands e-mail: [email protected] Library of Congress Control Number: 2004105112 The photo on the cover of the bull and bear in front of the Frankfurt Stock Exchange was taken by Professor Wolfgang Härdle. ISBN 978-3-540-21675-9 ISBN 978-3-662-10026-4 (eBook) DOI 10.1007/978-3-662-10026-4 Mathematics Subject Classification (2000): 62MI0, 62P05, 91B28, 91B84 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelbcrg GmbH. Violations are liable to prosecution under the German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Originallypublished by Springer-Verlag Berlin HeidelbcrgNewyotkin 2004 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Erich Kirchner, Heidelberg Typeset by the authors using a NEX macro package Printed on acid-free paper 40/3142at -5 43 2 1 0 Figure 0.1: Notes of a student for the exam of a course based on this book. Figure 0.2: Notes of a student for the exam of a course based on this book. Figure 0.3: Notes of a student for the exam of a course based on this book. Fig"" 0.4, No'es 01 a ,tndent 10' the ""am 01 a CO",'''' b .." ,i on ,hi, book. Figure 0.5: Notes of a student for the exam of a course based on this book. Preface Until about the 1970s, financial mathematics has been rather modest com pared with other mathematical disciplines. This changed rapidly after the path-breaking works of F. Black, M. Scholes, and R. Merton on derivative pricing, for which they received the Nobel prize of economics in 1997. Since 1973, the publication year of the famous Black and Scholes article, the im portance of derivative instruments in financial markets has not ceased to grow. Higher risks associated with, for example, flexible instead of fixed exchange rates after the fall of the Bretton Woods system required a risk management and the use of hedging instruments for internationally active companies. More recently, globalization and the increasingly complex depen dence of financial markets are reasons for using sophisticated mathematical and statistical methods and models to evaluate risks. The necessity to improve and develop the mathematical foundation of ex isting risk management was emphasized in the turbulent 1990s with, for example, the Asian crisis, the hedging disasters of Metallgesellschaft and Orange County, and the fall of the Long-Term Capital Management hedge fund (controlled by Merton and Scholes!). This saw the legislator obliged to take action. In continental Europe, this development is mainly influenced by the Basel Committee on Banking Supervision, whose recommendations form the basis in the European Union for legislation, with which financial insti tutions are obliged to do aglobaI, thorough risk management. As a result, there is an increasing demand for experts in financial engineering, who control risks internally, search for profitable investment opportunities and guarantee the obligations of legislation. In the future, such risk management is likely to become obligatory for other, deregulated markets such as telecommunica tion and energy markets. Being aware of the increasing price, volume, and credit risks in these markets, large companies usually have already created new departments dealing with asset and liability management as weIl as risk management. The present text is supposed to deli ver the necessary mathematical and sta tistical basis for a position in financial engineering. Our goal is to give a