||The Empirical Research of Asymmetry and Forecast Errors in the Implied Volatility Index
||Department of Banking and Finance
||This dissertation focuses on asymmetry and forecast errors in the implied volatility index and it contains three parts. The first part is titled “Relationships between the VIX and the S&P 500 Index: Threshold and asymmetric effects”, the second part is named “The financial implications of forecast errors in the implied volatility index”, and the last one is “Relationships between the implied volatility index and realized volatility: Forecast errors and informational content”. A brief introduction of these three parts can be described as follow:
The first part employs a TAR model to examine the VIX threshold effect and applies the ARJI model to investigate the various asymmetric effects in S&P 500 returns on changes in the VIX. The empirical results provide evidence of a high-low coefficient asymmetric effect, a rising-falling coefficient asymmetric effect and a high-low variance coefficient asymmetric effect. In particular, the coefficient asymmetric effects describe the phenomenon of extremely strong rallies and market bottoms in the high-fear regime when the VIX tends to fall. In addition, this study demonstrates that the jump intensity and the VIX have similar asymmetric effects in the different fear regimes.
The second part also applies the ARJI models that incorporate forecast errors to investigate the relationships between the changes in the implied volatility and the relevant determinant factors (especially forecast errors) in Taiwan. The empirical results provide evidence that the changes in the implied volatility are significantly affected by the contemporaneous returns, the lagged returns, the lagged changes in the implied volatility, the contemporaneous daily changes in the realized volatility and the lagged forecast errors. In particular, the extreme lagged forecast errors during the whole sample period and the lagged forecast errors during the financial crisis period have very various influences on the current changes in the implied volatility.
The final part adopts the orthogonality tests to examine whether the forecast errors are related to the informational content about past jump characteristics in Taiwan. The empirical results demonstrate that, if not taking forecast errors into account will lead to wrongly reject orthogonality so that the TVIX is not an efficient forecast for the future realized volatility due to forecast errors containing the relevant informational content, and vice versa. Of course, this study also demonstrates that the lagged forecast errors during the financial crisis period only have small influences on the current changes in the TVIX owing to abnormally informational content. This implies that the TVIX possesses the poor predictive ability during the financial crisis period.
||TABLE OF CONTENTS
ABSTRACT IN CHINESE ii
ABSTRACT IN ENGLISH iv
LIST OF TABLES ix
LIST OF FIGURES x
1. Introduction 1
1.1 Motivations 1
1.2 Objectives 4
1.3 Flow Chart 6
2. Literature Review 7
2.1 Literature on the relationships between the changes in the volatility index
and the corresponding stock market returns 7
2.2 Literature on the relationships between the implied volatility and the
realized volatility 9
2.3 Literature on informational content and forecast efficiency 12
3. Data Resources 14
3.1 Data resources in the Part I of this dissertation 14
3.2 Data resources in the Part II and Part III of this dissertation 14
4. Methodology 16
4.1 TAR model and ARJI model in the Part I of this dissertation 16
4.1.1 Threshold autoregressive model 16
4.1.2 ARJI model with the VIX threshold effect 17
4.2 ARJI model in the Part II of this dissertation 21
4.3 Orthogonality of forecast errors in the Part III of this dissertation 26
5. Empirical Results and Analysis 29
5.1 Empirical analysis of Part I - Relationships between the VIX and the
S&P 500 Index: Threshold and asymmetric effects 29
5.1.1 Descriptive statistics 29
5.1.2 Estimation for TAR model and asymmetric effects in series 30
5.1.3 Estimation of the ARJI model with the VIX threshold effect 31
5.2 Empirical Analysis of Part II - The financial implications of forecast
errors in the implied volatility index 38
5.2.1 Descriptive statistics 38
5.2.2 Comparison of models and determination of the superior model 41
5.2.3 Discussion of the financial implications in the superior model 45
5.2.4 Discussion of the financial implications of extreme forecast
errors during the whole sample period or of forecast errors
during the financial crisis period 48
5.3 Empirical analysis of Part III - Relationships between the implied
volatility index and realized volatility: Forecast errors and
informational content 53
5.3.1 Re-examining the superior model by orthogonality tests of
forecast errors 53
5.3.2 Discussion of the financial implications in forecast error
during the financial crisis period by orthogonality tests 56
6. Conclusions 61
6.1 Relationships between the VIX and the S&P 500 Index: Threshold
and asymmetric effects 61
6.2 The financial implications of forecast errors in the implied volatility index 62
6.3 Relationships between the implied volatility index and realized volatility:
Forecast errors and informational content 64
LIST OF TABLES
Table 5.1.1 Descriptive statistics 29
Table 5.1.2 Tests for the threshold effect in the VIX 31
Table 5.1.3 Empirical results and tests of the ARJI-M and ARJI-MV models 32
Table 5.1.4 Coefficient asymmetric effect for return and volatility 35
Table 5.1.5 Average and asymmetric effects for the jump intensity and the VIX 38
Table 5.2.1 Descriptive statistics 40
Table 5.2.2 Linear models 43
Table 5.2.3 ARJI model 44
Table 5.2.4 Linear (ARJI) models with extreme forecast errors or with forecast
errors during the event period 52
Table 5.3.1 ARJI models during the whole sample period 55
Table 5.3.2 Orthogonality tests by extracting the jump intensities in ARJI model
without forecast errors during the whole sample period 56
Table 5.3.3 Orthogonality tests by extracting the jump intensities in ARJI model
with forecast errors during the whole sample period 56
Table 5.3.4 Orthogonality tests by extracting the jump intensities in ARJI model
with forecast errors during the financial crisis period 59
Table 5.3.5 ARJI models with forecast errors during the whole of the sample
period or during the financial crisis period 60
LIST OF FIGURES
Figure 5.1.1 Daily S&P 500 Index and VIX 30
Figure 5.1.2 Daily Jump Intensity for S&P500 Returns and the VIX 37
Figure 5.2.1 TVIX and the 22-day moving average realized volatility 40
Figure 5.2.2 Forecast errors over the research period 41
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