Statistical Tools for Finance and Insurance
Statistical Tools for 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, t
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el Cížek • Wolfgang Ka rl Härdle • Rafał Weron (Eds.)
Statistical Tools for Finance and Insurance Second Ed ition
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Editors ˇ ížek Pavel C Tilburg University Dept. of Econometrics & OR P.O. Box 90153 5000 LE Tilburg, Netherlands [email protected]
Rafał Weron Wrocław University of Technology Institute of Organization and Management Wyb. Wyspia´ nskiego 27 50-370 Wrocław, Poland [email protected]
Wolfgang Karl Härdle Ladislaus von Bortkiewicz Chair of Statistics C.A.S.E. Centre for Applied Statistics and Economics School of Business and Economics Humboldt-Universität zu Berlin Unter den Linden 6 10099 Berlin, Germany [email protected]
The majority of chapters have quantlet codes in Matlab or R. These quantlets may be downloaded from http://ex tras.springer.com directly or via a link on http://springer.com/97 8 -3 -64 2 -18 061-3 and from www.quantlet.de. ISBN 978-3-642-18061-3 e-ISBN 978-3-642-18062-0 DOI 10.1007/978-3-642-18062-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011922138 © Springer-Verlag Berlin Heidelberg 2005, 2011 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 to prosecution under the German Copyright Law. 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: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents Contributors
9
Preface to the second edition
11
Preface
13
Frequently used notation
17
I
19
Finance
1 Models for heavy-tailed asset returns Szymon Borak, Adam Misiorek, and Rafal Weron 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Stable distributions . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Definitions and basic properties . . . . . . . . . . . . . . 1.2.2 Computation of stable density and distribution functions 1.2.3 Simulation of stable variables . . . . . . . . . . . . . . . 1.2.4 Estimation of parameters . . . . . . . . . . . . . . . . . 1.3 Truncated and tempered stable distributions . . . . . . . . . . 1.4 Generalized hyperbolic distributions . . . . . . . . . . . . . . . 1.4.1 Definitions and basic properties . . . . . . . . . . . . . . 1.4.2 Simulation of generalized hyperbolic variables . . . . . . 1.4.3 Estimation of parameters . . . . . . . . . . . . . . . . . 1.5 Empirical evidence . . . . . . .
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