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題名 以VIX指數偵測危機狀態之效果探討─TVTP方法之應用
A Study of the Effects on Detecting Financial Crisis State Using the VIX Index: Through the TVTP Approach
作者 戴天君
Tai, Tien Chun
貢獻者 陳威光
戴天君
Tai, Tien Chun
關鍵詞 波動度指數
金融危機
時序變動型馬可夫轉換模型
狀態轉換
VIX
Financial Crisis
TVTP
State Switching
日期 2012
上傳時間 1-Jul-2013 17:51:52 (UTC+8)
摘要 　　2008年全球爆發了金融海嘯，其後短短半年內，美國S&P500指數跌幅高達48%，令金融市場投資人一片譁然，連帶造成各項投資工具的價格重挫，並正式確立了美國市場的空頭格局。在此同時，具有「投資人恐慌指標」之稱的波動度指數(VIX)卻上漲了125%。VIX指數在歷史上幾次重大國際金融危機發生時點皆呈現大幅彈升與劇烈波動的現象；相較之下，在市場穩定、多頭氣氛濃厚時，VIX多處在低位且波動平緩。這兩種顯著差異的現象即VIX指數的狀態變化。
　　本研究目的之一為判斷VIX指數是否隨著前述兩種市場多空情形，而在自身結構上發生相對應的變化，並試圖了解狀態間轉換的時間點為何。本研究採用的方法為Filardo於1994年發表的「時序變動型馬可夫轉換模型(TVTP)」。此外，本研究更同時從統計角度及各模型實際績效表現，來比較納入額外變數資訊的TVTP模型是否優於Hamilton於1989年所提出的不包含額外資訊的「固定轉移機率馬可夫轉換模型(FTP)」。最後，本研究亦將歸納有助於提升模型能力的變數，以做為了解、甚至是判斷VIX指數變化的參考指標。
　　實證發現VIX指數可依據TVTP模型而區分為「低平均、低波動」與「高平均、高波動」兩種結構，且確實反映金融市場處於「平靜」或「危機」的狀態。本文也發現納入特定變數的TVTP模型不僅在統計角度上顯著優於FTP模型，利用TVTP模型偵測出的狀態變化時點進行買賣操作得到的實際績效亦優於FTP模型。本研究同時也歸納出觀察VIX指數動態時最具參考性的三大指標─追蹤S&P500指數的ETF價格變化、10年期信用價差和5年期信用價差，其中尤以5年期信用價差的模型在實際績效方面表現最佳，年化報酬率不僅優於FTP模型，亦超越同期大盤表現。
　　During the period from September, 2008 to March, 2009 after the financial crisis occurred, the S&P 500 index dropped about 48%, and global financial market suffered severe losses which established bear market firmly. Nevertheless, the “investor fear gauge”- CBOE Volatility Index rose 125% at the same time. Moreover, when some worldwide historic financial events or crises occurred, the VIX index also dramatically increased and fluctuated intensely. In contrast, while the market is tranquil or in a bull market, the level of VIX index keeps low and fluctuates smoothly; such structural change is called state switching.
　　One of the purposes in this study is to identify state switching in VIX index, and the time-varying transition probability Markov switching model (TVTP) Filardo developed in 1994 is used. Further, this paper investigates whether the effect of state identification by TVTP model incorporating exogenous variables is better than FTP model which is without extra variables. Finally, this paper generalizes what variables are beneficial for the model estimation and help observing VIX index.
　　The empirical results indicate that the VIX index can truly be identified as two states, and state switching indeed exists. Moreover, the TVTP models which incorporate respectively SPDR S&P500, 10-year credit spread, or 5-year credit spread are statistically significant better than the FTP model. Comparing all models through their practical performance, this paper finds six of nine TVTP models have higher return than FTP model, and even surpass the U.S. stock market index. Thus, this study concludes that the above three variables are the most significant useful indicators to observe the changes of VIX index, especially the 5-year credit spread.
參考文獻 Arias, G., Erlandsson, G., 2005. Improving Early Warning Systems with a Markov Switching Model - An Application to South-East Asian Crises. C.E.F.I. Working Paper No. 0502.
Baba, N., Sakurai, Y., 2011. Predicting Regime Switches in the VIX Index with Macroeconomic Variables. Applied Economics Letters, 18(15), 1415-1419.
Babecký, J., Havránek, T., Matějů, J., Rusnák, M., Šmídková, K., Vašíček, B., 2012. Leading Indicators of Crisis Incidence: Evidence from Developed Countries. Journal of International Money and Finance.
Bailey, W., Zheng L., Zhou Y., 2012. What Makes the VIX Tick? Social Science Research Network Working Paper Series, No.22/2012.
Berg, A., Pattillo, C., 1999. Predicting currency crises: The Indicators Approach and an Alternative. Journal of International Money and Finance, 18(4), 561-586.
Carr, P., Wu, L., 2006. A Tale of Two Indices. Journal of Derivatives, 13, 13-29.
Chen, S. S., 2009. Predicting the Bear Stock Market: Macroeconomic Variables as Leading Indicators. Journal of Banking & Finance, 33(2), 211-223.
Chen, S. W., 2012. Markov Switching Model: Applications to Economics and Finance. Compass.
Chen, W. K., 2010. Options: Theory, Practice, and Risk Management. Best-wise.
Connors, L., 2002. Timing You S&P Trades with the VIX. Futures: News, Analysis & Strategies for Futures, Options & Derivatives Traders, 31(7), 46.
Cumperayot, P., Keijzer, T., Kouwenberg, R., 2006. Linkages Between Extreme Stock Market and Currency Returns. Journal of International Money and Finance, 25(3), 528-550.
Ding, Z., 2012. An Implementation of Markov Regime Switching Model with Time Varying Transition Probabilities in Matlab. Social Science Research Network Working Paper Series.
Duca, Lo M., Peltonen, T., 2011. Macro-Financial Vulnerabilities and Future Financial Stress - Assessing Systemic Risks and Predicting Systemic Events. Social Science Research Network Working Paper Series, No.1311.
Dueker, M., 1997. Markov Switching in GARCH Processes and Mean-reverting Stockmarket Volatility. Journal of Business and Economic Statistics, 15, 26-34.
Dufrenot, G., Klaus, B., Malik, S., Vardoulakis, A. P., 2012. Credit Standards and Financial Institutions’ Leverage.
Engemann, K. M., Kliesen, K. L., Owyang, M. T., 2011. Do Oil Shocks Drive Business Cycles? Some U.S. and International Evidence. Macroeconomic Dynamics, 15(S3), 498-517.
Fabozzi, F. J., Martellini, L., Priaulet, P., 2006. Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies (Vol.143). Wiley.
Filardo, A. J., 1994. Business-Cycle Phases and Their Transitional Dynamics. Journal of Business & Economic Statistics, 12(3), 299-308.
Filardo, A. J., Gordon, S.F., 1998. Business Cycle Durations. Journal of Econometrics, 85(1), 99-123.
Filardo, A. J., Gordon, S.F., 1999. Business Cycle Turning Points: Two Empirical Business Cycle Model Approaches. pp. 1-32. Springer US.
Giot, P., 2003. The Asian Financial Crisis: the Start of a Regime Switch in Volatility. Social Science Research Network Working Paper Series.
Goldfeld, S. M., Quandt, R. E. (1973). A Markov Model for Switching Regressions. Journal of Econometrics, 1, 3-16.
Guo, W., Wohar M. E., 2006. Identifying Regime Changes in Market Volatility. Journal of Financial Research, 29, 79-93.
Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57, 357-384.
Hatzius, J., Hooper, P., Mishkin, F. S., Schoenholtz, K. L., Watson, M. W., 2010. Financial Conditions Indexes: A Fresh Look after the Financial Crisis. National Bureau of Economic Research.
Hill, J., Rattray, S., 2004. Volatility as a Tradable Asset: Using the VIX as a Market Signal, Diversifier and for Return Enhancement. Goldman, Sachs & Co.
Ismail, M. T., Isa, Z., 2008. Identifying Regime Shifts in Malaysian Stock Market Returns. International Research Journal of Finance and Economics, 15, 44-57.
Marcucci, J., 2005. Forecasting Stock Market Volatility with Regime-Switching GARCH Models. Studies in Nonlinear Dynamics & Econometrics, 9(4).
Mulvey, J. M., Zhao, Y. G., 2010. An Investment Model via Regime-Switching Economic Indicators. Working Paper.
Perlin, M., 2012. MS Regress - The MATLAB Package for Markov Regime Switching Models. Social Science Research Network Working Paper Series.
Quandt, R. E. (1958). Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regime. Journal of the American Statistical Association, 53, 873-880.
Ramzi, K., 2012. Estimating a MS-TVTP Model with MATLAB Software. Social Science Research Network Working Paper Series.
Romo, J. M., 2012. Volatility Regimes for the VIX Index. Revista de Economía Aplicada, 114-134.
Soylemez, A., 2012. Can Volatility Predict Future Stock Returns? Social Science Research Network Working Paper Series.
Sun, Y., Wu, X., 2009. A Nonparametric Study of Dependence Between S&P 500 Index and Market Volatility Index (VIX). In Beijing: EFMA symposium on Asian finance, 1-21.
Turner, M. C., Startz, R., Nelson, C. F. (1989). A Markov model of Heteroskedasticity, Risk, and Learning in the Stock Market. Journal of Financial Economics, 25, 3-22.
Wasim, A., & Bandi, K., 2011. Identifying Regime Shifts in Indian Stock Market: A Markov Switching Approach.
Weng, P. S., Chung, S. L., Tsai, W. C., Wang, Y. H., 2011. The Information Content of the S&P 500 Index and VIX Options on the Dynamics of the S&P 500 Index. Journal of Futures Markets, 31(12), 1170-1201.
Whaley, R. E., 1993. Derivatives on Market Volatility: Hedging Tools Long Overdue. Journal of Derivatives, 1, 71-84.
Whaley, R. E., 2000. The Investor Fear Gauge. Journal of Portfolio Management, 26(3), 12-17.
Whaley, R. E., 2008. Understanding the VIX. The Journal of Portfolio Management, 35(3), 98-105.
描述 碩士
國立政治大學
金融研究所
100352009
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100352009
資料類型 thesis
dc.contributor.advisor 陳威光zh_TW
dc.contributor.author (Authors) 戴天君zh_TW
dc.contributor.author (Authors) Tai, Tien Chunen_US
dc.creator (作者) 戴天君zh_TW
dc.creator (作者) Tai, Tien Chunen_US
dc.date (日期) 2012en_US
dc.date.accessioned 1-Jul-2013 17:51:52 (UTC+8)-
dc.date.available 1-Jul-2013 17:51:52 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2013 17:51:52 (UTC+8)-
dc.identifier (Other Identifiers) G0100352009en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58725-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 100352009zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 　　2008年全球爆發了金融海嘯，其後短短半年內，美國S&P500指數跌幅高達48%，令金融市場投資人一片譁然，連帶造成各項投資工具的價格重挫，並正式確立了美國市場的空頭格局。在此同時，具有「投資人恐慌指標」之稱的波動度指數(VIX)卻上漲了125%。VIX指數在歷史上幾次重大國際金融危機發生時點皆呈現大幅彈升與劇烈波動的現象；相較之下，在市場穩定、多頭氣氛濃厚時，VIX多處在低位且波動平緩。這兩種顯著差異的現象即VIX指數的狀態變化。
　　本研究目的之一為判斷VIX指數是否隨著前述兩種市場多空情形，而在自身結構上發生相對應的變化，並試圖了解狀態間轉換的時間點為何。本研究採用的方法為Filardo於1994年發表的「時序變動型馬可夫轉換模型(TVTP)」。此外，本研究更同時從統計角度及各模型實際績效表現，來比較納入額外變數資訊的TVTP模型是否優於Hamilton於1989年所提出的不包含額外資訊的「固定轉移機率馬可夫轉換模型(FTP)」。最後，本研究亦將歸納有助於提升模型能力的變數，以做為了解、甚至是判斷VIX指數變化的參考指標。
　　實證發現VIX指數可依據TVTP模型而區分為「低平均、低波動」與「高平均、高波動」兩種結構，且確實反映金融市場處於「平靜」或「危機」的狀態。本文也發現納入特定變數的TVTP模型不僅在統計角度上顯著優於FTP模型，利用TVTP模型偵測出的狀態變化時點進行買賣操作得到的實際績效亦優於FTP模型。本研究同時也歸納出觀察VIX指數動態時最具參考性的三大指標─追蹤S&P500指數的ETF價格變化、10年期信用價差和5年期信用價差，其中尤以5年期信用價差的模型在實際績效方面表現最佳，年化報酬率不僅優於FTP模型，亦超越同期大盤表現。		zh_TW
dc.description.abstract (摘要) 　　During the period from September, 2008 to March, 2009 after the financial crisis occurred, the S&P 500 index dropped about 48%, and global financial market suffered severe losses which established bear market firmly. Nevertheless, the “investor fear gauge”- CBOE Volatility Index rose 125% at the same time. Moreover, when some worldwide historic financial events or crises occurred, the VIX index also dramatically increased and fluctuated intensely. In contrast, while the market is tranquil or in a bull market, the level of VIX index keeps low and fluctuates smoothly; such structural change is called state switching.
　　One of the purposes in this study is to identify state switching in VIX index, and the time-varying transition probability Markov switching model (TVTP) Filardo developed in 1994 is used. Further, this paper investigates whether the effect of state identification by TVTP model incorporating exogenous variables is better than FTP model which is without extra variables. Finally, this paper generalizes what variables are beneficial for the model estimation and help observing VIX index.
　　The empirical results indicate that the VIX index can truly be identified as two states, and state switching indeed exists. Moreover, the TVTP models which incorporate respectively SPDR S&P500, 10-year credit spread, or 5-year credit spread are statistically significant better than the FTP model. Comparing all models through their practical performance, this paper finds six of nine TVTP models have higher return than FTP model, and even surpass the U.S. stock market index. Thus, this study concludes that the above three variables are the most significant useful indicators to observe the changes of VIX index, especially the 5-year credit spread.		en_US
dc.description.tableofcontents 1. Introduction 1
2. Literature Review 7
2.1 Ideas and Characteristics of VIX 7
2.2 Variables for Predicting Financial Crisis and Economic Recession 9
2.3 State Switching Issue and Application of Markov Switching Model 18
3. Methodology 22
3.1 Fixed Transition Probability (FTP) Model 22
3.2 Time-varying Transition Probability (TVTP) Model 23
3.3 Modification of TVTP Model in Practice 29
4. Empirical Results 32
4.1 Data 32
4.2 Process of Model Construction and Selection 33
4.3 Comparing TVTP Models with FTP Model in Practical Performance 41
5. Conclusion 48
References 52
Appendix A: Estimated Parameters of Generalized TVTP Models 56
Appendix B: Details about Practical Performance Examination 60
Appendix C: Smoothed Probability Comparison 70		zh_TW
dc.format.extent 1894252 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100352009en_US
dc.subject (關鍵詞) 波動度指數zh_TW
dc.subject (關鍵詞) 金融危機zh_TW
dc.subject (關鍵詞) 時序變動型馬可夫轉換模型zh_TW
dc.subject (關鍵詞) 狀態轉換zh_TW
dc.subject (關鍵詞) VIXen_US
dc.subject (關鍵詞) Financial Crisisen_US
dc.subject (關鍵詞) TVTPen_US
dc.subject (關鍵詞) State Switchingen_US
dc.title (題名) 以VIX指數偵測危機狀態之效果探討─TVTP方法之應用zh_TW
dc.title (題名) A Study of the Effects on Detecting Financial Crisis State Using the VIX Index: Through the TVTP Approachen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Arias, G., Erlandsson, G., 2005. Improving Early Warning Systems with a Markov Switching Model - An Application to South-East Asian Crises. C.E.F.I. Working Paper No. 0502.
Baba, N., Sakurai, Y., 2011. Predicting Regime Switches in the VIX Index with Macroeconomic Variables. Applied Economics Letters, 18(15), 1415-1419.
Babecký, J., Havránek, T., Matějů, J., Rusnák, M., Šmídková, K., Vašíček, B., 2012. Leading Indicators of Crisis Incidence: Evidence from Developed Countries. Journal of International Money and Finance.
Bailey, W., Zheng L., Zhou Y., 2012. What Makes the VIX Tick? Social Science Research Network Working Paper Series, No.22/2012.
Berg, A., Pattillo, C., 1999. Predicting currency crises: The Indicators Approach and an Alternative. Journal of International Money and Finance, 18(4), 561-586.
Carr, P., Wu, L., 2006. A Tale of Two Indices. Journal of Derivatives, 13, 13-29.
Chen, S. S., 2009. Predicting the Bear Stock Market: Macroeconomic Variables as Leading Indicators. Journal of Banking & Finance, 33(2), 211-223.
Chen, S. W., 2012. Markov Switching Model: Applications to Economics and Finance. Compass.
Chen, W. K., 2010. Options: Theory, Practice, and Risk Management. Best-wise.
Connors, L., 2002. Timing You S&P Trades with the VIX. Futures: News, Analysis & Strategies for Futures, Options & Derivatives Traders, 31(7), 46.
Cumperayot, P., Keijzer, T., Kouwenberg, R., 2006. Linkages Between Extreme Stock Market and Currency Returns. Journal of International Money and Finance, 25(3), 528-550.
Ding, Z., 2012. An Implementation of Markov Regime Switching Model with Time Varying Transition Probabilities in Matlab. Social Science Research Network Working Paper Series.
Duca, Lo M., Peltonen, T., 2011. Macro-Financial Vulnerabilities and Future Financial Stress - Assessing Systemic Risks and Predicting Systemic Events. Social Science Research Network Working Paper Series, No.1311.
Dueker, M., 1997. Markov Switching in GARCH Processes and Mean-reverting Stockmarket Volatility. Journal of Business and Economic Statistics, 15, 26-34.
Dufrenot, G., Klaus, B., Malik, S., Vardoulakis, A. P., 2012. Credit Standards and Financial Institutions’ Leverage.
Engemann, K. M., Kliesen, K. L., Owyang, M. T., 2011. Do Oil Shocks Drive Business Cycles? Some U.S. and International Evidence. Macroeconomic Dynamics, 15(S3), 498-517.
Fabozzi, F. J., Martellini, L., Priaulet, P., 2006. Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies (Vol.143). Wiley.
Filardo, A. J., 1994. Business-Cycle Phases and Their Transitional Dynamics. Journal of Business & Economic Statistics, 12(3), 299-308.
Filardo, A. J., Gordon, S.F., 1998. Business Cycle Durations. Journal of Econometrics, 85(1), 99-123.
Filardo, A. J., Gordon, S.F., 1999. Business Cycle Turning Points: Two Empirical Business Cycle Model Approaches. pp. 1-32. Springer US.
Giot, P., 2003. The Asian Financial Crisis: the Start of a Regime Switch in Volatility. Social Science Research Network Working Paper Series.
Goldfeld, S. M., Quandt, R. E. (1973). A Markov Model for Switching Regressions. Journal of Econometrics, 1, 3-16.
Guo, W., Wohar M. E., 2006. Identifying Regime Changes in Market Volatility. Journal of Financial Research, 29, 79-93.
Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57, 357-384.
Hatzius, J., Hooper, P., Mishkin, F. S., Schoenholtz, K. L., Watson, M. W., 2010. Financial Conditions Indexes: A Fresh Look after the Financial Crisis. National Bureau of Economic Research.
Hill, J., Rattray, S., 2004. Volatility as a Tradable Asset: Using the VIX as a Market Signal, Diversifier and for Return Enhancement. Goldman, Sachs & Co.
Ismail, M. T., Isa, Z., 2008. Identifying Regime Shifts in Malaysian Stock Market Returns. International Research Journal of Finance and Economics, 15, 44-57.
Marcucci, J., 2005. Forecasting Stock Market Volatility with Regime-Switching GARCH Models. Studies in Nonlinear Dynamics & Econometrics, 9(4).
Mulvey, J. M., Zhao, Y. G., 2010. An Investment Model via Regime-Switching Economic Indicators. Working Paper.
Perlin, M., 2012. MS Regress - The MATLAB Package for Markov Regime Switching Models. Social Science Research Network Working Paper Series.
Quandt, R. E. (1958). Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regime. Journal of the American Statistical Association, 53, 873-880.
Ramzi, K., 2012. Estimating a MS-TVTP Model with MATLAB Software. Social Science Research Network Working Paper Series.
Romo, J. M., 2012. Volatility Regimes for the VIX Index. Revista de Economía Aplicada, 114-134.
Soylemez, A., 2012. Can Volatility Predict Future Stock Returns? Social Science Research Network Working Paper Series.
Sun, Y., Wu, X., 2009. A Nonparametric Study of Dependence Between S&P 500 Index and Market Volatility Index (VIX). In Beijing: EFMA symposium on Asian finance, 1-21.
Turner, M. C., Startz, R., Nelson, C. F. (1989). A Markov model of Heteroskedasticity, Risk, and Learning in the Stock Market. Journal of Financial Economics, 25, 3-22.
Wasim, A., & Bandi, K., 2011. Identifying Regime Shifts in Indian Stock Market: A Markov Switching Approach.
Weng, P. S., Chung, S. L., Tsai, W. C., Wang, Y. H., 2011. The Information Content of the S&P 500 Index and VIX Options on the Dynamics of the S&P 500 Index. Journal of Futures Markets, 31(12), 1170-1201.
Whaley, R. E., 1993. Derivatives on Market Volatility: Hedging Tools Long Overdue. Journal of Derivatives, 1, 71-84.
Whaley, R. E., 2000. The Investor Fear Gauge. Journal of Portfolio Management, 26(3), 12-17.
Whaley, R. E., 2008. Understanding the VIX. The Journal of Portfolio Management, 35(3), 98-105.		zh_TW