Consistency Problems for Heath-Jarrow-Morton Interest Rate Models
The book is written for a reader with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, such as provided by Revuz and Yor (Continuous Martingales and Brownian Motion, Springer 1991). It gives a shor
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Damir Filipovic
Consistency Problems for Heath-Jarrow-Morton Interest Rate Models
Springer
Author Damir Filipovic Department of Mathematics ETH-Zentrum CH-8092 Zurich E-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Filipovic, Darnir: Consistency problems for Heath-larrow-Morton interest rate models / Darnir Filipovic. Berlin; Heidelberg; New York; Barcelona; Hong Kong; London ; Milan; Paris ; Singapore; Tokyo: Springer, 2001 (Lecture notes in mathematics; 1760) ISBN 3-540-41493-2
Mathematics Subject Classification (2000): 91 B28, 60H 15, 93B29 ISSN 0075-8434 ISBN 3-540-41493-2 Springer-Verlag 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a part of Springer Science+Business Media http://www.springer.de
© Springer-Verlag Berlin Heidelberg 2001 Printed in Germany Typesetting: Camera-ready TEX output by the authors SPIN: 11310815 41/3111-54321- Printed on acid-free paper
Preface
Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up by a finite number of traded assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinitedimensional variable which is not directly observable. On the empirical side this necessitates curvefitting methods for the daily estimation of the term structure. Pricing models on the other hand, are usually built upon stochastic factors representing the term structure in a finitedimensional state space, making them computationally tractable. This research monograph brings together curvefitting methods and factor models for the term structure of interest rates within the HeathJarrowMorton (henceforth HJM) framework [35], which basically unifies all continuous interest rate models. We provide appropriate consistency conditions and explore some important examples. The HJM framework can be seen as a generic description of the arbitragefree movements of the forward curve (the term structure of forward rates), driven by a Brownian motion. The noarbitrage requirement leads to a restriction on the drift of any single forward rate process (HJM drift condition). The (infinitedimensional) state variable in an HJM model is the entire forward curve. As such, any initial forward curve can be taken as model input. But, by the HJM d
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