Pricing of Derivatives on Mean-Reverting Assets
The topic of this book is the development of pricing formulae for European style derivatives on assets with mean-reverting behavior, especially commodity derivatives. For this class of assets, convenience yield effects lead to mean-reversion under the ris
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Björn Lutz
Pricing of Derivatives on Mean-Reverting Assets
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Dr. Björn Lutz Hauck & Aufhäuser Asset Management GmbH Löwengrube 18 80333 München Germany [email protected]
ISSN 0075-8442 ISBN 978-3-642-02908-0 e-ISBN 978-3-642-02909-7 DOI 1 0.1007/978-3-642-02909-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009930466 © Springer-Verlag Berlin Heidelberg 2010 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. 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: SPi Publishing Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Inge and Karl
Foreword
As already mentioned by Lo and Wang (1995) there is an apparent paradox if we derive standard option pricing formulae for an underlying mean-reverting drift. While the drift has an influence on the long-run behavior of the underlying, the option price becomes independent of the drift of the price process itself. Using the continuous-time pricing framework this leads to option prices which are much too large for more distant maturities. One possible solution for this paradox is the assumption that the market is incomplete. As shown by Ross (1997), in an incomplete market the mean reversion remains in the drift of the risk-adjusted process under the equivalent martingale measure. However, mean reversion in the drift complicates the solution process for option pricing considerably. Lutz contributes to this research in several respects. Using state-of-the-art Fourier inversion techniques he extends the mean-reverting one-factor diffusion setting of Schwartz (1997) and Ross (1997) and discusses processes with stochastic volatility, different jump components, a stochastic equilibrium level and deterministic seasonalities. This leads to new and rather complex models, where the resulting Riccati systems are difficult to solve. While giving new analytic solutions in some cases Lutz shows that numerical procedures for the Riccati systems are often superior in terms of numerical efficiency. I recommend this research monograph to everybody who deals with the specific peculiarities of mean-reversion in option pricing. T¨ubingen, May 2009
Rainer Sch¨obel
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Acknowledgements
The research presented in this Ph.D. thesis has b
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