Stochastic Volatility in Financial Markets Crossing the Bridge to Co
Stochastic Volatility in Financial Markets presents advanced topics in financial econometrics and theoretical finance, and is divided into three main parts. The first part aims at documenting an empirical regularity of financial price changes: the occurre
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Dynamic Modeling and Econometrics in Economics and Finance VOLUME 3
Series Editors Stefan Mittnik, University of Kiel, Germany Willi Semmler, University of Bielefeld, Germany and New School for Social Research, USA
STOCHASTIC VOLATILITY IN FINANCIAL MARKETS CROSSING THE BRIDGE TO CONTINUOUS TIME
Fabio Fornari Bank of Italy
and Antonio Mele Universite du Littoral and THEMA, Universite de Paris X
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SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data Fornari, Fabio Stochastie volatility in finaneial markets : erossing the bridge to eontinuous timei Fabio Fornari and Antonio Mele p. em. -- (Dynamic modeling and eeonometries in eeonomies and finanee;
v.3) Includes bibliographieal referenees and index. ISBN 978-1-4613-7045-1 ISBN 978-1-4615-4533-0 (eBook) DOI 10.1007/978-1-4615-4533-0 1. Finanee--Econometrie models. 2. Capital market--Eeonometric models. 3. Stochastic analysis. 1. Mele, Antonio. II. Title. III. Series.
HG 173 .F67 2000 332'.0I'5195--de21
00-028741
Copyright © 2000 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers, New York in 2000 Softcover reprint ofthe hardcover Ist edition 2000 AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC
Printed on acid-free paper.
A Alessandra F.F. A Alessia e Florence A.M.
CONTENTS List of figures ........................................................... xi List of tables . .......................................................... xiii Preface ................................................................. . xv Chapter 1 - Introduction ................................................ l 1.1 Background and aims of the monograph ................................. 1 1.2 Empirical models in discrete time ....................................... 7 1.2.1 The basic models .................................................. 7 1.2.2 Extensions ......................................................... 8 1.2.3 Volatility asymmetries: ramifications .............................. 11 1.2.4 Diffusions as ARCH models approximations ....................... 14 1.3 Theoretical issues ...................................................... 16 1.3.1 European option pricing .......................................... 16 1.3.2 The term structure of interest rates ............................... 20 1.4 Statistical inference .................................................... 23 1.5 Plan ................................................................... 29 Chapter 2 - Continuous time behavior of non linear ARCH models . ......................................................... 31 2.1 Introduction ........................................................... 31 2.2 Approximation results for a general class of non linear ARCH models ... 31 2.3 Interpretation of the moment c
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