Affine Diffusions and Related Processes: Simulation, Theory and Applications
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially s
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Aurélien Alfonsi
Affine Diffusions and Related Processes: Simulation, Theory and Applications
B&SS – Bocconi & Springer Series Series Editors: Lorenzo Peccati • Sandro Salsa (Editors-in-Chief) Carlo A. Favero • Peter Müller • Eckhard Platen • Wolfgang J. Runggaldier
Volume 6
More information about this series at http://www.springer.com/series/8762
Aurélien Alfonsi
Affine Diffusions and Related Processes: Simulation, Theory and Applications
123
Aurélien Alfonsi CERMICS Ecole Nationale des Ponts et Chaussées Champs-sur-Marne, France
ISSN 2039-1471 ISSN 2039-148X (electronic) B&SS – Bocconi & Springer Series ISBN 978-3-319-05220-5 ISBN 978-3-319-05221-2 (eBook) DOI 10.1007/978-3-319-05221-2 Library of Congress Control Number: 2015938922 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
The development of affine processes in modelling has shadowed the expansion of financial mathematics ever since the pioneering works of Black and Scholes [20] and Merton [106] in the 1970s. These processes have various desirable features, the main one being an explicit description of their marginal laws as a function of their parameters. This property plays a key role in enabling the fitting of affine models to market data within a limited computational time, which has made them popular for the pricing and hedging of derivatives. Surprisingly, up until the late 1990s, there were very few works on the simulation of these affine processes; this can be partly explained by the fact that the two simplest affine diffusions can be sampled exactly by using either a Gaussian or a noncentral chi-square distribution, despite the simulation of the latter is rather time consuming. It is, however, important to generate samples of these affine diffusio
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