Modelling Stock Market Volatility: Bridging the Gap to Continuous Time

505 Pages·1996·5.8 MB·English

by  Peter H. Rossi

MODELLING
STOCK MARKET
VOLATILITY
Bridging the Gap co
Continuous Time
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M O D E L L I N G
S T O C K M A R K E T
V O LATI L I T Y
Bridging the Gap to
Continuous Time
Edited by
Peter E. Rossi
Graduate School of Business
The University of Chicago
Chicago, Illinois
ACADEMIC PRESS
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Library of Congress Cataloging-in-Publication Data
Modelling stock market volatility : bridging the gap to continuous
time / edited by Peter Rossi.
p. cm.
Includes index.
ISBN 0-12-598275-5 (alk. paper)
1. Stocks--Prices--Mathematical models. I. Rossi, Peter E.
(Peter Eric), date.
HG4636.M63 1996
332.63'222--dc20 96-26267
CIP
PRINTED IN THE UNITED STATES OF AMERICA
96 97 98 99 00 01 BB 9 8 7 6 5 4 3 2 1
CONTENTS
CONTRIBUTORS ix
INTRODUCTION xi
I
UNDERSTANDING AND SPECIFYING
THE DISCRETE TIME MODEL
I. Modelling Stock Market Volatility Changes 3
DANIEL B. NELSON
2. Stationarity and Persistence in the
GARCH(I,I) Model 17
DANIEL B. NELSON
3. Conditional Heteroskedasticity in Asset Returns:
A New Approach 37
DANIEL B. NELSON
vi CONTENTS
4. Good News, Bad News, Volatility, and Betas 65
PHILLIP A. BRAUN, DANIEL B. NELSON,A ND ALAIN IVl. SUNIER
II
CONTINUOUS TIME LIMITS AND
OPTIMAL FILTERING FOR ARCH MODELS
5. ARCH Models as Diffusion Approximations 99
DANIEL B. NELSON
6. Filtering and Forecasting with Misspecified ARCH
Models I: Getting the Right Variance with the
Wrong Model 129
DANIEL B. NELSON
7. Filtering and Forecasting with Misspecified
ARCH Models I1: Making the Right Forecast
with the Wrong Model 157
DANIEL B. NELSON AND DEAN P. FOSTER
8. Asymptotic Filtering Theory for Univariate
ARCH Models 193
DANIEL B. NELSON AND DEAN P. FOSTER
9. Asymptotic Filtering Theory for Multivariate
ARCH Models 241
DANIEL B. NELSON
10. Continuous Record Asymptotics for
Rolling Sample Variance Estimators 291
DEAN P. FOSTER AND DANIEL B. NELSON
III
SPECIFICATION AND ESTIMATION OF
CONTINUOUS TIME PROCESSES
I I. Estimating Diffusion Models of Stochastic Volatility 333
ROBERT F. ENGLE AND GARY G. J. LEE
12. Specification Analysis of Continuous
Time Models in Finance 357
A. RONALD GALLANT AND GEORGE TAUCHEN
CONTENTS VIooI
13. Back to the Future: Generating Moment Implications
for Continuous-Time Markov Processes 385
jOSl~
LARS PETER HANSEN AND ALEXANDRE SCHEINKMAN
14. Nonparametric Pricing of Interest Rate
Derivative Securities 427
YAClNE A'iT-SAHALIA
INDEX 467
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CONTRIBUTORS
Numbers in parentheses indicate the pages on which the author's contributions begin.
Yacine Ait-Sahalia (427) Graduate School of Business, University of
Chicago, Chicago, Illinois 60637.
Tim Bollerslev (xi) Department of Finance, Northwestern University,
Evanston, Illinois 60208.
PhiUip A. Braun (65) J. L. Kellogg Graduate School of Management,
Northwestern University, Evanston, Illinois 60208.
Robert F. Engle (333) Department of Economics, University of California,
San Diego, La JoUa, California 92093.
Dean P. Foster (157, 193, 291) Wharton School, University of Pennsylva-
nia, Philadelphia, Pennsylvania 19104.
A. Ronald Gallant (357) Department of Economics, University of North
Carolina, Chapel Hill, North Carolina 27599.
Lars Peter Hansen (385) Department of Economics, University of Chicago,
Chicago, Illinois 60637.
ix