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系統識別號 U0002-0807201011402800
中文論文名稱 隱含波動指標不對稱性與預測誤差之實證研究
英文論文名稱 The Empirical Research of Asymmetry and Forecast Errors in the Implied Volatility Index
校院名稱 淡江大學
系所名稱(中) 財務金融學系博士班
系所名稱(英) Department of Banking and Finance
學年度 98
學期 2
出版年 99
研究生中文姓名 林奇泰
研究生英文姓名 Chi-Tai Lin
學號 895530128
學位類別 博士
語文別 英文
口試日期 2010-07-03
論文頁數 71頁
口試委員 指導教授-邱建良
指導教授-李命志
委員-梁發進
委員-黃博怡
委員-黃彥聖
委員-林蒼祥
中文關鍵字 VIX  不對稱性效果  TAR模型  ARJI模型  預測誤差  隱含波動  TVIX  真實波動  資訊內涵 
英文關鍵字 VIX  Asymmetric Effect  TAR Model  ARJI Model  Forecast Errors  Implied Volatility  TVIX  Realized Volatility  Informational Content 
學科別分類 學科別社會科學商學
中文摘要 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。
英文摘要 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.
論文目次 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
參考文獻 Äijö, J. (2008) Implied volatility term structure linkages between VDAX, VSMI and VSTOXX volatility indices, Global Finance Journal, 18, 290-302.
Akgiray, V. and Booth, G. (1987) Compound distribution models of stock returns: an empirical comparison, Journal of Financial Research, 10, 269-280.
Andersen, T. G. and Bollerslev, T. (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review, 39, 885-905.
Andersen, T. G., Bollerslev, T. and Lange, S. (1999) Forecasting financial market volatility: Sampling frequency vis-a-vis forecast horizon, Journal of Empirical Finance, 6, 457-477.
Andersen, T. G., Bollerslev, T. and Diebold, F. X. (2007) Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility, Review of Economics and Statistics, 89, 701-720.
Badshah, I. U. (2009) Asymmetric return-volatility relation, volatility transmission and implied volatility indexes, Working Paper, Hanken School of Economics in Finland.
Bakshi, G., Cao, C. and Chen, Z. (1997) Empirical performance of alternative options pricing models, Journal of Finance, 52, 2003-2049.
Bali, T. G. and Peng, L. (2006) Is there a risk-return tradeoff? Evidence from high-frequency data, Journal of Applied Econometrics, 21, 1169-1198.
Bali, T. G. and Weinbaum, D. (2007) A conditional extreme value volatility estimator based on high-frequency returns, Journal of Economic Dynamics and Control, 31, 361-397.
Ball, C. A. and Torous, W. N. (1985) On jumps in stock returns, Journal of Financial and Quantitative Analysis, 10, 337-351.
Barndorff-Nielsen, O. E. and Shephard, N. (2004) Power and bi-power variation with stochastic volatility and jumps, Journal of Financial Econometrics, 2, 1-37.
Becker, R., Clements, A. and White, S. (2006) On the informational efficiency of S&P 500 implied volatility, North American Journal of Economics and Finance, 17, 139-153.
Becker, R., Clements, A. and White, S. (2007) Does implied volatility provide any information beyond that captured in model-based volatility forecasts?, Journal of Banking and Finance, 31, 2535-2549.
Becker, R., Clements, A. and McClelland, A. (2009) The jump component of S&P 500 volatility and the VIX index, Journal of Banking & Finance, 33, 1033-1038.
Blair, B. J., Poon, S. and Taylor, S. J. (2001) Forecasting S&P 100 volatility: The incremental information content of implied volatilities and high-frequency index returns, Journal of Econometrics, 105, 5-26.
Bollerslev, T. and Zhou, H. (2006) Volatility puzzles: A simple framework for gauging return-volatility regressions, Journal of Econometrics, 131, 123-150.
Chan, W. H. and Maheu, J. M. (2002) Conditional jump dynamics in stock market return, Journal of Business & Economic Statistics, 20, 377-389.
Chan W. H. (2003) A correlated bivariate Poisson jump model for foreign exchange, Empirical Economics, 28, 669-685.
Chicago Board Options Exchange (2009) CBOE Volatility Index-VIX, White Paper (retrieved from http://www.cboe.com/micro/vix/vixwhite.pdf).
Chiou, J. S., Wu, P. S. and Lee, M. C. (2006) Variation of interest-rate parity and its asymmetry on stock return in a jump-diffusion process, Applied Financial Economics, 16, 1309-1316.
Chiu, C. L., Lee, M. C. and Hung, J. C. (2005) Estimation of Value-at-Risk under jump dynamics and asymmetric information, Applied Financial Economics, 15, 1095-1106.
Chiu, C. L., Chiang, S. M. and Kao F. (2006) The relationship between the S&P 500 spot and futures indices: Brothers or cousins?, Applied Financial Economics, 16, 405-412.
Christensen, B. J. and Prabhala, N. R. (1998) The relation between implied and realized volatility, Journal of Financial Economics, 50, 125-150.
Corrado, C. J. and Miller, T. W. (2005) The forecast quality of CBOE implied volatility indexes, Journal of Futures Markets, 25, 339-373.
Daniel, K. D., Hirshleifer, D. and Subrahmanyam, A. (1998) Investor psychology and security market under- and overreactions, Journal of Finance, 53, 1839-1885.
Das, S. R. and Sundaram, R. K. (1999) Of smiles and smirks: A term structure perspective, Journal of Financial and Quantitative Analysis, 34, 211-239.
DeBondt, Werner F. M., and Thaler, R. H. (1985) Does the stock market overreact?, Journal of Finance, 40, 793-808.
Dennis, P., Mayhew, S. and Stivers, C. (2006) Stock returns, implied volatility innovations, and the asymmetric volatility phenomenon, Journal of Financial and Quantitative Analysis, 41, 381-406.
Donaldson, R. G. and Kamstra, M. J. (2005) Volatility forecasts, trading volume, and the ARCH versus option-implied volatility trade-off, Journal of Financial Research, 28, 519-538.
Dotsis, G., Psychoyios, D. and Skiadopoulos, G. (2007) An empirical comparison of continuous-time models of implied volatility indices, Journal of Banking and Finance, 31, 3584-3603.
Dreman, D. N. (1982) The New Contrarian Investment Strategy, New York: Random House.
Dumas, B., Fleming, J. and Whaley, R. E. (1998) Implied volatility functions: Empirical tests, Journal of Finance, 53, 2059-2106.
Ederington, L. and Guan, W. (2005) The information frown in option prices, Journal of Banking and Finance, 29, 1429-1457.
Engle, R. F. (1990) Discussion: stock market volatility and crash of ’87, Review of Financial Studies, 48, 103-106.
Engle, R. F. and Ng, V. K. (1993) Measuring and testing the impact of news on volatility, Journal of Finance, 48, 1749-1778.
Eraker, B., Johannes, M. and Polson, N. (2003) The impact of jumps in volatility and returns, Journal of Finance, 58, 1269-1300.
Fleming, J. (1998) The quality of market volatility forecasts implied by S&P100 index option prices, Journal of Empirical Finance, 5, 317-345.
Fleming, J., Ostdiek, B. and Whaley, R. E. (1995) Predicting stock market volatility: A new measure, The Journal of Futures Market, 15, 265-302.
Ghysels, E., Santa-Clara, P. and Valkanov, R. (2005) There is a risk-return tradeoff after all, Journal of Financial Economics, 76, 509-548.
Giot, P. (2005) Relationships between implied volatility indexes and stock index returns: Are implied volatility indexes leading indicators?, The Journal of Portfolio Management, 31, 92-100.
Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993) On the relation between the expected value and the volatility on the nominal excess returns on stocks, Journal of Finance, 48, 1779-1801.
Hansen, B. E. (1996) Inference when a nuisance parameter is not identified under the null hypothesis, Econometrica, 64, 413-430.
Hansen, B. E. (1997) Inference in TAR models, Studies in Nonlinear Dynamics and Econometrics, 2, 1-14.
Hansen, L. P. and Hodrick, R. J. (1980) Forward rates as optimal predictors of future spot rates: An econometric analysis, Journal of Political Economy, 88, 829-853.
Hibbert, A. M., Daigler, R. T. and Dupoyet, B. (2008) A behavioral explanation for the negative asymmetric return-volatility relation, Journal of Banking and Finance, 32, 2254-2266.
Jarrow, R. A., and Rosenfeld, E. R. (1984) Jump risks and the intertemporal capital asset pricing model, The Journal of Business, 57, 337-351.
Jiang, G. J. and Tian, Y. S. (2003) Model-free implied volatility and its information content, Unpublished Manuscript.
Jorion, P. (1988) On jump processes in the foreign exchange and stock markets, Review of Financial Studies, 1, 427-445.
Low, C. (2004) The fear and exuberance from implied volatility of S&P 100 index options, Journal of Business, 77, 527-546.
Lundblad, C. T. (2007) The risk return tradeoff in the long-run: 1836-2003, Journal of Financial Economics, 85, 123-150.
Maheu, J. M. and McCurdy, T. H. (2004) News arrival, jump dynamics and volatility components for individual stock returns, Journal of Finance, 59, 755-793.
Mayhew, S. and Stivers, C. (2003) Stock return dynamics, option volume, and the information content of implied volatility, Journal of Futures Markets, 23, 615-646.
Nelson, D. B. (1991) Conditional heteroskedasticity in asset returns: A new approach, Econometric, 59, 347-370.
Newey, W. K. and West, K. D. (1987) Hypothesis testing with efficient method of moments estimation, International Economic Review, 28 ,777-787.
Nikkinen, J. and Sahlström, P. (2004) International transmission of uncertainty implicit in stock index option prices, Global Finance Journal, 15, 1-15.
Nikkinen, J., Sahlström, P. and Vähämaa, S. (2006) Implied volatility linkages among major European currencies, Journal of International Financial Markets, Institutions, and Money, 16, 87-103.
Pan, J. (2002) The jump-risk premia implicit in options: Evidence from an integrated time-series study, Journal of Financial Economics, 63, 3-50.
Pong, S., Shackleton, M. B., Taylor, S. J. and Xu, X. (2004) Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models, Journal of Banking and Finance, 28, 2541-2563.
Selcuk, F. (2005) Asymmetric stochastic volatility in emerging stock markets, Applied Financial Economics, 15, 867-874.
Sepp, A. (2008) VIX option pricing in a jump-diffusion model, RISK, 21, 84-89.
Shefrin, H. (2008) Ending the management illusion: How to drive business results using the principles of behavioral finance, McGraw Hill.
Simon, D. P. (2003) The Nasdaq volatility index during and after the bubble, Journal of Derivatives, 11, 9-24.
Skiadopoulos, G. (2004) The Greek implied volatility index: Construction and properties, Applied Financial Economics, 14, 1187-1196.
Tan, K. (2002) Fixated on the VIX, Barron's, July 29.
Wagner, N. and Szimayer, A. (2004) Local and spillover shocks in implied market volatility: Evidence from the U.S. and Germany, Research in international Business and Finance, 18, 237-251.
Whaley, R. E. (2000) The investor fear gauge, The Journal of Portfolio Management, 26, 12-17.
Whaley, R. E. (2009) Understanding the VIX, The Journal of Portfolio Management, 3, 98-105.
Wong, W. K. and Tu, A. H. (2009) Market imperfections and the information content of implied and realized volatility, Pacific-Basin Finance Journal, 17, 58-79.
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