Table Of ContentEmpirical Studies on Volatility in International Stock Markets
Dynamic Modeling and Econometrics in Economics
and Finance
VOLUME6
Series Editors
Stefan Mittnik, University of Kiel, Germany
Willi Semmler, University ofB ielefeld, Germany and
New School for Social Research, U.S.A.
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Empirical Studies on Volatility
in International Stock Markets
by
Eugenie M.J.H. Hol
lNG Group Credit Risk Management,
Amsterdam, The Netherlands
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-5375-9 ISBN 978-1-4757-5129-1 (eBook)
DOI 10.1007/978-1-4757-5129-1
Primed on acid-free paper
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© 2003 Springer Science+ Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2003
Softcover reprint of the hardcover I st edition 2003
No part of this work may be reproduced, stored in a retrieval system, or transmitted
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Well, I don’t think
getting to the top is all
that important. You
can always have
another go. The things
you remember after a
trip are not standing
on the summit but
what went on while you
were on the route.
Mo Anthoine -
mountaineer
Contents
List of Figures xi
List of Tables xiv
1. Introduction 1
2. Asset Return Volatility Models 7
2.1 Empirical Stylised Facts of Stock Index Return Series 8
2.2 Time-Varying Volatility Models 12
2.2.1 GARCH Models 13
2.2.2 SV Models 16
2.3 Empirical Applications of Time-Varying Volatility
Models 19
3. The Stochastic Volatility in Mean Model:
Empirical evidence from international stock markets 27
3.1 Introduction 27
3.2 The Stochastic Volatility in Mean Model 28
3.3 Some Theory on the Relationship between Returns and
Volatility 30
3.4 Data 33
3.5 Estimation Results for the SVM Model and Some
Diagnostics 36
3.6 Some Comparisons with GARCH-M Estimation Results 42
3.7 Summary and Conclusions 46
4. Forecasting with Volatility Models 49
4.1 Volatility Models and Their Forecasts 49
4.2 An Empirical Study of Six International Stock Indices 52
vii
viii Empirical Studies on Volatility in International Stock Markets
4.2.1 Data and Methodology 54
4.2.2 Forecasting Results 58
5. Implied Volatility 63
5.1 The Black-Scholes Option Pricing Model 63
5.2 Forecasting with Implied Volatility: Empirical evidence 67
6. Forecasting theVariabilityofStock IndexReturns
with Stochastic Volatility Models and Implied Volatility 71
6.1 Introduction 71
6.2 Model Specifications 73
6.3 Data Description and Empirical In-Sample Results 77
6.3.1 Data 77
6.3.2 Empirical In-Sample Results 81
6.4 Volatility Forecasting Methodology 84
6.4.1 Stochastic Volatility Model Forecasts 84
6.4.2 SVX+ and SIV Model Forecasts 85
6.4.3 Measuring Predictive Forecasting Ability 85
6.4.4 Intraday Volatility 87
6.5 Out-of-Sample Results 89
6.5.1 The Parameters Estimates of the SV Model 89
6.5.2 Empirical Out-of-Sample Forecasting Results 91
6.6 Summary and Conclusions 96
7. Stock Index Volatility Forecasting with
High Frequency Data 99
7.1 Introduction 99
7.2 Stock Return Data and Volatility 101
7.2.1 Data 101
7.2.2 Intraday Volatility 103
7.3 Realised Volatility Models 108
7.3.1 Unobserved Components OU Type Stochastic
Volatility Models 108
7.3.2 ARFIMA Models 110
7.4 Daily Time-Varying Volatility Models 112
7.4.1 Daily SV Model 112
7.4.2 Daily SV Model with Intraday Volatility 114
7.4.3 Daily GARCH(1,1) Model 115
7.4.4 Daily GARCH(1,1) Model with Intraday
Volatility 116
Contents ix
7.5 Forecasting Methodology and Evaluation Criteria 117
7.5.1 Forecasting Methodology 117
7.5.2 Evaluation Criteria 117
7.6 Empirical Results 119
7.6.1 In-Sample Results 119
7.6.2 Out-of-Sample Results 122
7.7 Summary and Conclusions 126
8. Conclusions 129
Appendices 135
A.Estimation of the SVM Model 135
A.1 Model 135
A.2 Likelihood Evaluation Using Importance Sampling 136
A.3 Approximating Gaussian Model Used For Importance
Sampling 137
A.4 Monte Carlo Evidence of Estimation Procedure 139
B. Estimation of the SVX Models 145
B.1 The SVX Model in State Space Form 145
B.2 Parameter Estimation by Simulated Maximum
Likelihood 146
B.3 Computational Implementation 147
C.Data and Programs 149
Bibliography 151
Index 159
List of Figures
2.1 Returns for the Financial Times All Share Index (UK)
at (i) daily, (ii) weekly and (iii) monthly frequencies
between 02/01/75 and 30/09/00 9
2.2 Autocorrelationcoefficientsforthesquaredreturns,SV
and GARCH models of the Financial Times All Share
Index (UK) at (i) daily and (ii) weekly frequencies 25
3.1 Excess returns for the (i) FT All Share Index (UK)
and (ii) S&P Composite Stock Index (US) between
02/01/75 and 31/12/98 and for the (iii) Topix Stock
Index (Japan) between 04/01/88 and 31/12/98. 35
4.1 Volatility forecasts produced by the RW, SV and
GARCH(1,1) model. 51
4.2 Daily returns on the (i) FT All Share, (ii) S&P Com-
posite, (iii) Topix, (iv) DAX, (v)CAC40 and(vi) AEX
Stock Index over the period 04/01/88 to 31/12/99 55
6.1 Daily (i) returnsand (ii) squared returns(truncated at
100) on the Standard & Poor’s 100 index and (iii) the
VIX index between 02/01/86 and 29/06/01 79
6.2 Sample first-order autocorrelation coefficients and
summed cross-products multiplied by 2 as defined
in equation (6.17) for sampling frequencies f =
5,10,15,30,65,130,195 and 390. 89
6.3 Parameterestimates(i)φ,(ii)σ2 and(iii)σ∗2 oftheSV
η
model and (iv) the variance of the estimation sample
based on the previous 9 years of data. 90
xi
xii Empirical Studies on Volatility in International Stock Markets
6.4 Daily squared returns, intraday volatility based on 10-
minute squared returns and the VIX implied volatil-
ity together with the one-day ahead volatility forecasts
of the SV, SVX+ and SIV model for the Standard &
Poor’s 100 indexover theperiod06/01/97 to 29/06/01
based on a 9-year rolling window sample and with av-
erage annual volatilities given in percentages. 95
7.1 The daily (i) return series R and (ii) squared return
t
seriesR2 oftheStandard&Poor’s100stockindexover
t
the period 06/01/97 to 29/12/00 103
7.2 Time series and histograms with normal approxima-
tions for the Standard & Poor’s 100 stock index re-
alised volatility measures (i-a) σ˜2 and (ii-a) σ˜2 and
t,1 t,3
their logarithmic counterparts (ii-a) lnσ˜2 and (ii-b)
t,1
lnσ˜2 over the period 06/01/97 to 29/12/00 106
t,3
7.3 One-day ahead volatility forecasts of the (i) UC-RV
and ARFIMA-RV, (ii) SV and GARCH, and (iii) SVX
and GX models against the realised volatility measure
σ˜2 (RV) over the period 13/03/00 to 06/06/00. 125
t,3
A.1 Monte Carlo results for the standard SV model. 141
A.2 Monte Carlo results for the SVM model. 142
