Statistical Tools for Finance and Insurance
Statistical Tools in Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field of
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el Cížek • Wolfgang Härdle • Rafał Weron
Statistical Tools for Finance and Insurance
123
ˇ Pavel Cížek Tilburg University Dept. of Econometrics & OR P.O. Box 90153 5000 LE Tilburg, Netherlands e-mail: [email protected]
Rafał Weron Wrocław University of Technology Hugo Steinhaus Center Wyb. Wyspia´ nskiego 27 50-370 Wrocław, Poland e-mail: [email protected]
Wolfgang Härdle Humboldt-Universität zu Berlin CASE – Center for Applied Statistics and Economics Institut für Statistik und Ökonometrie Spandauer Straße 1 10178 Berlin, Germany e-mail: [email protected]
This book is also available as e-book on www.i-xplore.de. Use the licence code at the end of the book to download the e-book. Library of Congress Control Number: 2005920464
Mathematics Subject Classification (2000): 62P05, 91B26, 91B28
ISBN 3-540-22189-1 Springer Berlin Heidelberg New York 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. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany 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. Typesetting by the authors Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: design & production GmbH, Heidelberg Printed on acid-free paper 46/3142YL – 5 4 3 2 1 0
Contents
Contributors
13
Preface
15
I
19
Finance
1 Stable Distributions
21
Szymon Borak, Wolfgang H¨ ardle, and Rafal Weron 1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
1.2
Definitions and Basic Characteristic . . . . . . . . . . . . . . .
22
1.2.1
Characteristic Function Representation . . . . . . . . .
24
1.2.2
Stable Density and Distribution Functions . . . . . . . .
26
1.3
Simulation of α-stable Variables . . . . . . . . . . . . . . . . . .
28
1.4
Estimation of Parameters . . . . . . . . . . . . . . . . . . . . .
30
1.4.1
Tail Exponent Estimation . . . . . . . . . . . . . . . . .
31
1.4.2
Quantile Estimation . . . . . . . . . . . . . . . . . . . .
33
1.4.3
Characteristic Function Approaches . . . . . . . . . . .
34
1.4.4
Maximum Likelihood Method . . . . . . . . . . . . . . .
35
Financial Applications of Stable Laws . . . . . . . . . . . . . .
36
1.5
2
Contents
2 Extreme Value Analysis and Copulas
45
Krzysztof Jajuga and Daniel
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