[[alternative]]隱含波動指標不對稱性與預測誤差之實證研究

博士[[abstract]]本論文著重在隱含波動指標不對稱性與預測誤差之實證研究，共包含三個部份，分別為「VIX與S&P 500指數之關係：門檻與不對稱性效果」、「隱含波動指標預測誤差之財務意涵」與「隱含波動指標與真實波動之關係：預測誤差與資訊內涵」，在此將三部份的內容簡述如下。 第一部分研究使用了TAR模型以檢查VIX門檻效果，以及應用ARJI模型檢測S&P 500股票指數報酬對VIX變動的不對稱性。實證結果證明了具有高與低恐慌係數的不對稱效果、VIX上升與下降係數的不對稱效果及高與低恐慌變異數係數的不對稱效果。特別是係數的不對稱性效果，描述了當在高恐慌區間VIX指標傾向於下降時，極端強烈的復甦與市場谷底之現象發生。另外，本研究證明了跳躍強度與VIX指標在不同的恐慌區間有相似的不對稱性。 第二部份本文應用了ARJI模型併入了預測誤差，以檢測台灣隱含波動的變動與相關決定因子(特別是預測誤差)之關係。實證結果證明了隱含波動的變動，顯著地受到當期報酬、落後報酬、隱含波動的落後變動、真實波動的同期(日)變動與落後預測誤差的影響。特別是在全觀察期的極端落後預測誤差與金融風暴期間的落後預測誤差，對隱含波動的當期變動有著非常不同的影響效果。 第三部份本文採用了正交檢定，以檢驗在臺灣是否預測誤差與過去的跳躍特徵之資訊內涵有關?實證結果發現，假如模型不納入預測誤差將會導致錯誤地拒絕正交，以致於因為預測誤差包含了相關的資訊內涵，造成TVIX對未來真實波動的預測不是很有效率，反之亦然。當然，本研究亦證明了金融危機期間由於具有異常的資訊內涵，造成落後的預測誤差對TVIX的當期變動只有很小的影響效果，因此這裡隱含了TVIX在金融危機期間具有不好的預測能力。[[abstract]]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.[[tableofcontents]]TABLE OF CONTENTS Page ACKNOWLEDGEMENTS i 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 Bibiography 65 LIST OF TABLES Page 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 Page 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[[note]]學號: 895530128, 學年度: 9