Pricing of Bond Options Unspanned Stochastic Volatility and Random F
RWT Award 2008! For his excellent monograph, Detlef Repplinger won the RWT Reutlinger Wirtschaftstreuhand GMBH award in June 2008. A major theme of this book is the development of a consistent unified model framework for the evaluation of bond options. In
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Detlef Repplinger
Pricing of Bond Options Unspanned Stochastic Volatility and Random Field Models
Dr. Detlef Repplinger Man Investments AG Huobstrasse 3 8808 Pfäffikon SZ Switzerland [email protected]
ISBN 978-3-540-70721-9
e-ISBN 978-3-540-70729-5
DOI 10.1007/978-3-540-70729-5 Lecture Notes in Economics and Mathematical Systems ISSN 0075-8442 Library of Congress Control Number: 2008931347 © 2008 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 permissions for use must always be obtained from Springer-Verlag. Violations are liable for 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: WMX Design GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com
Foreword
There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way: ”We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises.” Repplinger contributes to the research in this area with a new systematic approach. He develops a generalized Edgeworth expansion technique, called Integrated Edgeworth Expansion (IEE), to overcome the aforementioned consistency problem. Together with a ’state of the art’ Fractional Fourier Transform technique (FRFT) for the pricing of caps and floors this method is applied to price swaptions within a set of ’up to date’ multidimensional stochastic interest rate models. Beside the traditional multi-factor Heath-Jarrow-Morton models, term structure models driven by random fields and models with unspanned stochastic volatility are successfully covered. Along the way some new closed form solutions are presented. I am rather impressed by the results of this thesis and I am sure, that this monograph will be most useful for researchers and practitioners in the field. T¨ubingen, May 2008
Rainer Sch¨obel
v
Acknowledgements
This Ph.D. thesis has been prepared and accepted by the College of Economics and Business Administ
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