Tools for Computational Finance
This book is very easy to read and one can gain a quick snapshot of computational issues arising in financial mathematics. Researchers or students of the mathematical sciences with an interest in finance will find this book a very helpful and gentle guide
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Tools for Computational Finance Fourth Edition
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Prof. Dr. Rüdiger U. Seydel Universität Köln Mathematisch-Naturwiss. Fakultät Mathematisches Institut Weyertal 86-90 50931 Köln Germany [email protected]
ISBN: 978-3-540-92928-4 DOI: 10.1007/978-3-540-92929-1
e-ISBN: 978-3-540-92929-1
Library of Congress Control Number: 2008943076
c 2002, 2004, 2006, 2009 Springer-Verlag Berlin Heidelberg 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.
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Preface to the First Edition
Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation. Fast and accurate numerical algorithms have become essential tools to price financial derivatives and to manage portfolio risks. The required methods aggregate to the new field of Computational Finance. This discipline still has an aura of mysteriousness; the first specialists were sometimes called rocket scientists. So far, the emerging field of computational finance has hardly been discussed in the mathematical finance literature. This book attempts to fill the gap. Basic principles of computational finance are introduced in a monograph with textbook character. The book is divided into four parts, arranged in six chapters and seven appendices. The general organization is Part I (Chapter 1): Financial and Stochastic Background Part II (Chapters 2, 3): Tools for Simulation Part III (Chapters 4, 5, 6): Partial Differential Equations for Options Part IV (Appendices A1...A7): Further Requisits and Additional Material. The first chapter introduces fundamental concepts of financial options and of stochastic calculus. This provides the financial and stochastic background needed to follow this book. The chapter explains the terms and the functioning of standard options, and continues
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