The large number of already available textbooks on stochastic calculus with specific applications to finance requires a justification for another contribution to this subject. The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to Föllmer, who showed that one can develop Ito's calculus "pathwise" as an exercise in real analysis. The text opens to students interested in finance a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader is supposed only to be familiar with elementary real analysis (e.g. Taylor's Theorem) and basic probability theory. The text is also useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis.

Zusammenfassung
to Stochastic Calculus for Finance A New Didactic Approach With 6 Figures 123 Prof. Dr. Dieter Sondermann Department of Economics University of Bonn Adenauer Allee 24 53113 Bonn, Germany E-mail: sondermann@uni-bonn. de ISBN-10 3-540-34836-0 Springer Berlin Heidelberg New York ISBN-13 978-3-540-34836-8 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, speci?cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro?lm 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 is a part of Springer Science+Business Media springeronline. com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this pub- cation does not imply, even in the absence of a speci?c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by author Cover: Erich Kirchner, Heidelberg Production: LE-T X, Jelonek, Schmidt & Vöckler GbR, Leipzig E SPIN 11769675 Printed on acid-free paper 42/3100 5 4 3 2 1 0 To Freddy, Hans and Marek, who patiently helped me to a deeper understanding of stochastic calculus.

Inhalt
Preliminaries.- to Itô-Calculus.- The Girsanov Transformation.- Application to Financial Economics.- Term Structure Models.- Why Do We Need Itô-Calculus in Finance?.- Appendix: Itô Calculus Without Probabilities.