Financial Derivatives Modeling

This book gives a comprehensive introduction to the modeling of financial derivatives, covering all major asset classes (equities, commodities, interest rates and foreign exchange) and stretching from Black and Scholes' lognormal modeling to current-day r

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Christian Ekstrand

Financial Derivatives Modeling

123

Christian Ekstrand Stockholm Sweden [email protected]

ISBN 978-3-642-22154-5 e-ISBN 978-3-642-22155-2 DOI 10.1007/978-3-642-22155-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011936378 c Springer-Verlag Berlin Heidelberg 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

The purpose of this book is to give a comprehensive introduction to the modeling of financial derivatives, covering the major asset classes and stretching from Black and Scholes’ lognormal modeling to current-day research on skew and smile models. The intended reader has a solid mathematical background and works, or plans to work, at a financial institution such as an investment bank or a hedge fund. The aim of the book is to equip the reader with modeling tools that can be used in the (future) work involving derivatives pricing, trading, or risk management. The field of derivatives modeling is extensive and to keep the book within a reasonable size, certain sacrifices have been made. For instance, the implementation of models is not discussed as this can be viewed as an art rather than science and is therefore an ungrateful subject for a text book. Minor asset classes, such as inflation products, and asset classes that require specific mathematical tools, e.g., credit and mortgage products, have been left out. Furthermore, the financial basics are covered at a faster pace than in other introductory books to the area. For example, the martingale theory is summarized in a compact appendix, and the introduction to the Black–Scholes model is done by working directly in continuous space-time, in contrast to the pedagogical approach of initially reviewing the binomial model. This enables us to quickly go beyond the Black–Scholes framework and thereby focus on skew and smile models and on derivatives in specific asset classes. The book is divided into four parts. The first part consists of Chaps. 1–4 and contains the general framework of derivatives pricing. This part is essential for the understanding of the rest of the book. An exception is Ch