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題名 預測S&P500指數實現波動度與VIX－ 探討VIX、VIX選擇權與VVIX之資訊內涵
The S&P 500 Index Realized Volatility and VIX Forecasting - The Information Content of VIX, VIX Options and VVIX
作者 黃之澔
貢獻者 陳威光<br>林靖庭
Chen, Wei Kuang<br>Lin, Ching Ting
黃之澔
關鍵詞 VIX 選擇權
VVIX
資訊內涵
S&P500指數實現波動度
動態轉換模型
風險中立動差
VIX Options
VVIX
Information Content
S&P 500 Realized Volatility
Regime Switching Model
Risk Neutral Moments
日期 2014
上傳時間 1-Jul-2015 14:45:06 (UTC+8)
摘要 波動度對於金融市場影響甚多，同時為金融資產定價的重要參數以及市場穩\n定度的衡量指標，尤其在金融危機發生時，波動度指數的驟升反映資產價格震盪。\n本篇論文嘗試捕捉S&P500 指數實現波動度與VIX變動率未來之動態，並將VIX、\nVIX 選擇權與VVIX 納入預測模型中，探討其資訊內涵。透過研究S&P500 指數\n實現波動度，能夠預測S&P500 指數未來之波動度與報酬，除了能夠觀察市場變\n動，亦能使未來選擇權定價更為準確；而藉由模型預測VIX，能夠藉由VIX 選\n擇權或VIX 期貨，提供避險或投資之依據。文章採用2006 年至2011 年之S&P500\n指數、VIX、VIX 選擇權與VVIX 資料。\n在 S&P500 指數之實現波動度預測當中，本篇論文的模型改良自先前文獻，\n結合實現波動度、隱含波動度與S&P500 指數選擇權之風險中立偏態，所構成之\n異質自我回歸模型(HAR-RV-IV-SK model)。論文額外加入VIX 變動率以及VIX指數選擇權之風險中立偏態作為模型因子，預測未來S&P500 指數實現波動度。\n研究結果表示，加入VIX 變動率作為S&P500 指數實現波動度預測模型變數後，\n可增加S&P500 指數實現波動度預測模型之準確性。\n在 VIX 變動率預測模型之中，論文採用動態轉換模型，作為高低波動度之\n下，區分預測模型的方法。以VIX 過去的變動率、VIX 選擇權之風險中立動差\n以及VIX 之波動度指數(VVIX)作為變數，預測未來VIX 變動率。結果顯示動態\n轉換模型能夠提升VIX 預測模型的解釋能力，並且在動態轉換模型下，VVIX 與\nVIX 選擇權之風險中立動差，對於VIX 預測具有相當之資訊隱涵於其中。
This paper tries to capture the future dynamic of S&P 500 index realized\nvolatility and VIX. We add the VIX change rate and the risk neutral skewness of VIX\noptions into the Heterogeneous Autoregressive model of Realized Volatility, Implied\nVolatility and Skewness (HAR-RV-IV-SK) model to forecast the S&P 500 realized\nvolatility. Also, this paper uses the regime switching model and joins the VIX, risk\nneutral moments of VIX options and VVIX variables to raise the explanatory ability\nin the VIX forecasting. The result shows that the VIX change rate has additional\ninformation on the S&P 500 realized volatility. By using the regime switching model,\nthe VVIX and the risk neutral moments of VIX options variables have information\ncontents in VIX forecasting. These models can be used for hedging or investment\npurposes.
參考文獻 Akaya O., Senyuzc Z., Yoldas E., 2013. Hedge fund contagion and risk-adjusted returns: a\nMarkov-switching dynamic factor approach. Journal of Empirical Finance 22, 16–29.\nBakshi, Kapadia, Madan, 2003. Stock return characteristics, skew laws, and the differential pricing of\nindividual equity options. The Reviews of Financial Studies, Vol. 16, 101 - 143.\nBauwensa L., Dufaysa A., Rombouts J.V.K., 2014. Marginal likelihood for Markov-switching and\nchange-point GARCH models. Journal of Econometrics 178, 508–522.\nBekaerta G., Hoerova M., 2014. The VIX, the variance premium and stock market volatility. Journal of\nEconometrics 183, 181–192.\nByun S.J., Kim J.S., 2013. The information content of risk-neutral skewness for volatility forecasting.\nJournal of Empirical Finance 23, 142–161.\nChalamandaris G., Rompolis L.S., 2012. Exploring the role of the realized return distribution in the\nformation of the implied volatility smile. Journal of Banking & Finance 36, 1028–1044.\nChang B.Y, Christoffersen P., Jacobs K., 2013. Market skewness risk and the cross section of stock\nreturns. Journal of Financial Economics 107, 46–68.\nChuanga W.I., Huangb T.C., Lin B.H., 2013. Predicting volatility using the Markov- switching\nmultifractal model: Evidence from S&P 100 index and equity options. North American Journal of\nEconomics and Finance 25, 168– 187.\nChung S.L., TsaiW.C., Wang Y.H., Weng P.S., 2011.The information content of the S&P 500 index and\nVIX options on the dynamics of the S&P 500 index. Journal of Futures Markets, Vol. 31, No. 12,\n1170–1201.\nConrad J., Dittmar R.F., Ghysels E., 2013. Ex Ante Skewness and Expected Stock Returns. Journal of\nFinance Vol. 68, No. 1.\nCordisa S.A., Kirby C., 2014. Discrete stochastic autoregressive volatility. Journal of Banking &\nFinance 43, 160–178.\nCorsi, F, 2009.A simple approximate long-memory model of realized volatility, Journal of Financial\nEconometrics,Vol.7, Issue 2, 174-196\nDueker M., Neely C.J., 2007. Can Markov switching models predict excess foreign exchange returns?\nJournal of Banking & Finance 31, 279–296.\nFernandesa M.,. Medeirosc M.C., Scharth M., 2014. Modeling and predicting the CBOE market\nvolatility index. Journal of Banking & Finance 40, 1–10.\nGatheral, 2008. Consistent Modeling of SPX and VIX options.\nGray S.F, 1996. Modeling the conditional distribution of interest rates as a regime-switching process.\nJournal of Financial Economics 42, 27 - 62.\nHamilton J.D., 1989. A new approach to the economic analysis of nonstationary time series and the\nbusiness cycle. Econometrica Vol. 57, No. 2, 357 - 384.\nHamilton J.D., 1990.Analysis of time series subject to changes in regime. Journal of Econometrics 45,\n39-70.\nKanniainena J., Lina B., Yang H., 2014. Estimating and using GARCH models with VIX data for option\nvaluation. Journal of Banking & Finance 43, 200–211.\nKhalifaa A.A.A, Hammoudehb S., Otranto E., 2014. Patterns of volatility transmissions within regime\nswitching across GCC and global markets. International Review of Economics and Finance 29,\n512–524.\nKim C.J, 1994. Dynamic linear models with Markov-switching. Journal of Econometrics 60, l-22.\nLin Y.N., 2013. VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility\nderivatives valuation. Journal of Banking & Finance 37, 4432–4446.\nLiua X., Margaritisb D., Wang P., 2012. Stock market volatility and equity returns: Evidence from a\ntwo-state Markov-switching model with regressors. Journal of Empirical Finance 19, 483–496.\nMiaoa W.C., Wub C.C., Su Y.K., 2013. Regime-switching in volatility and correlation structure using\nrange-based models with Markov-switching. Economic Modelling 31, 87–93.\nNeumanna M., Skiadopoulos G., 2013.Predictable dynamics in higher order risk-neutral\nmoments:evidence from the S&P 500 options. Journal of Financial and Quantitative Analysis, Vol.\n48, Issue 03, 947 - 977.\nOnan M., Salih A., Burze Yasar, 2014. Impact of macroeconomic announcements on implied volatility\nslope of SPX options and VIX. Finance Research Letters 11, 454–462.\nPan Q., Li Y., 2013. Testing volatility persistence on Markov switching stochastic volatility models.\nEconomic Modelling 35, 45–50.\nPatrick S., Stewart M., 2002. Risk-neutral skewness: evidence from stock options. Journal of Financial\n& Quantitative Analysis, Vol. 37, 471.\nRaggia D., Bordignon S., 2012. Long memory and nonlinearities in realized volatility: A Markov\nswitching approach. Computational Statistics and Data Analysis 56, 3730–3742.\nRaggia, Bordignon, 2012. Long memory and nonlinearities in realized volatility: A Markov switching\napproach. Computational Statistics & Data Analysis,Vol. 56, Issue 11, Pages 3730–3742\nRossia A., Giampiero, 2006. Volatility estimation via hidden Markov models. Journal of Empirical\nFinance 13, 203– 230.\nZhou Y., 2014. Modeling the joint dynamics of risk-neutral stock index and bond yield volatilities.\nJournal of Banking & Finance 38, 216–228
描述 碩士
國立政治大學
金融研究所
102352010
103
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102352010
資料類型 thesis
dc.contributor.advisor 陳威光<br>林靖庭zh_TW
dc.contributor.advisor Chen, Wei Kuang<br>Lin, Ching Tingen_US
dc.contributor.author (Authors) 黃之澔zh_TW
dc.creator (作者) 黃之澔zh_TW
dc.date (日期) 2014en_US
dc.date.accessioned 1-Jul-2015 14:45:06 (UTC+8)-
dc.date.available 1-Jul-2015 14:45:06 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2015 14:45:06 (UTC+8)-
dc.identifier (Other Identifiers) G0102352010en_US
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=85002-
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) 102352010zh_TW
dc.description (描述) 103zh_TW
dc.description.abstract (摘要) 波動度對於金融市場影響甚多，同時為金融資產定價的重要參數以及市場穩\n定度的衡量指標，尤其在金融危機發生時，波動度指數的驟升反映資產價格震盪。\n本篇論文嘗試捕捉S&P500 指數實現波動度與VIX變動率未來之動態，並將VIX、\nVIX 選擇權與VVIX 納入預測模型中，探討其資訊內涵。透過研究S&P500 指數\n實現波動度，能夠預測S&P500 指數未來之波動度與報酬，除了能夠觀察市場變\n動，亦能使未來選擇權定價更為準確；而藉由模型預測VIX，能夠藉由VIX 選\n擇權或VIX 期貨，提供避險或投資之依據。文章採用2006 年至2011 年之S&P500\n指數、VIX、VIX 選擇權與VVIX 資料。\n在 S&P500 指數之實現波動度預測當中，本篇論文的模型改良自先前文獻，\n結合實現波動度、隱含波動度與S&P500 指數選擇權之風險中立偏態，所構成之\n異質自我回歸模型(HAR-RV-IV-SK model)。論文額外加入VIX 變動率以及VIX指數選擇權之風險中立偏態作為模型因子，預測未來S&P500 指數實現波動度。\n研究結果表示，加入VIX 變動率作為S&P500 指數實現波動度預測模型變數後，\n可增加S&P500 指數實現波動度預測模型之準確性。\n在 VIX 變動率預測模型之中，論文採用動態轉換模型，作為高低波動度之\n下，區分預測模型的方法。以VIX 過去的變動率、VIX 選擇權之風險中立動差\n以及VIX 之波動度指數(VVIX)作為變數，預測未來VIX 變動率。結果顯示動態\n轉換模型能夠提升VIX 預測模型的解釋能力，並且在動態轉換模型下，VVIX 與\nVIX 選擇權之風險中立動差，對於VIX 預測具有相當之資訊隱涵於其中。zh_TW
dc.description.abstract (摘要) This paper tries to capture the future dynamic of S&P 500 index realized\nvolatility and VIX. We add the VIX change rate and the risk neutral skewness of VIX\noptions into the Heterogeneous Autoregressive model of Realized Volatility, Implied\nVolatility and Skewness (HAR-RV-IV-SK) model to forecast the S&P 500 realized\nvolatility. Also, this paper uses the regime switching model and joins the VIX, risk\nneutral moments of VIX options and VVIX variables to raise the explanatory ability\nin the VIX forecasting. The result shows that the VIX change rate has additional\ninformation on the S&P 500 realized volatility. By using the regime switching model,\nthe VVIX and the risk neutral moments of VIX options variables have information\ncontents in VIX forecasting. These models can be used for hedging or investment\npurposes.en_US
dc.description.tableofcontents 1. Introduction 1\n2. Literature Review 2\n2.1 VIX, VIX Options and VVIX 2\n2.2 Risk Neutral Skewness 3\n2.3 HAR-RV-IV-SK Model 4\n2.4 Volatility Forecasting 4\n2.5 Regime Switching Model 5\n3. Data 6\n3.1 CBOE Data 6\n3.2 Realized Volatility Data 7\n3.3 VIX Options Data 7\n3.4 Risk Neutral Moments of VIX Options 7\n3.5 VVIX Data 10\n4. S&P 500 Realized Volatility Forecasting 12\n4.1 Single Variable Regression Testing 12\n4.2 Methodology 13\n4.3 Results 18\n4.4 Residual Analysis 20\n5. VIX Forecasting 23\n5.1 Single Variable Regression Testing 24\n5.2 Regime Switching Model 25\n5.3 VIX Forecasting Models 26\n5.4 VIX Forecasting Results 31\n5.5 Model Analysis 33\n6. Conclusion 36\nAppendix I – The formula of VIX 38\nAppendix II – The formula of risk neutral moments of VIX options 39zh_TW
dc.format.extent 2684306 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102352010en_US
dc.subject (關鍵詞) VIX 選擇權zh_TW
dc.subject (關鍵詞) VVIXzh_TW
dc.subject (關鍵詞) 資訊內涵zh_TW
dc.subject (關鍵詞) S&P500指數實現波動度zh_TW
dc.subject (關鍵詞) 動態轉換模型zh_TW
dc.subject (關鍵詞) 風險中立動差zh_TW
dc.subject (關鍵詞) VIX Optionsen_US
dc.subject (關鍵詞) VVIXen_US
dc.subject (關鍵詞) Information Contenten_US
dc.subject (關鍵詞) S&P 500 Realized Volatilityen_US
dc.subject (關鍵詞) Regime Switching Modelen_US
dc.subject (關鍵詞) Risk Neutral Momentsen_US
dc.title (題名) 預測S&P500指數實現波動度與VIX－ 探討VIX、VIX選擇權與VVIX之資訊內涵zh_TW
dc.title (題名) The S&P 500 Index Realized Volatility and VIX Forecasting - The Information Content of VIX, VIX Options and VVIXen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Akaya O., Senyuzc Z., Yoldas E., 2013. Hedge fund contagion and risk-adjusted returns: a\nMarkov-switching dynamic factor approach. Journal of Empirical Finance 22, 16–29.\nBakshi, Kapadia, Madan, 2003. Stock return characteristics, skew laws, and the differential pricing of\nindividual equity options. The Reviews of Financial Studies, Vol. 16, 101 - 143.\nBauwensa L., Dufaysa A., Rombouts J.V.K., 2014. Marginal likelihood for Markov-switching and\nchange-point GARCH models. Journal of Econometrics 178, 508–522.\nBekaerta G., Hoerova M., 2014. The VIX, the variance premium and stock market volatility. Journal of\nEconometrics 183, 181–192.\nByun S.J., Kim J.S., 2013. The information content of risk-neutral skewness for volatility forecasting.\nJournal of Empirical Finance 23, 142–161.\nChalamandaris G., Rompolis L.S., 2012. Exploring the role of the realized return distribution in the\nformation of the implied volatility smile. Journal of Banking & Finance 36, 1028–1044.\nChang B.Y, Christoffersen P., Jacobs K., 2013. Market skewness risk and the cross section of stock\nreturns. Journal of Financial Economics 107, 46–68.\nChuanga W.I., Huangb T.C., Lin B.H., 2013. Predicting volatility using the Markov- switching\nmultifractal model: Evidence from S&P 100 index and equity options. North American Journal of\nEconomics and Finance 25, 168– 187.\nChung S.L., TsaiW.C., Wang Y.H., Weng P.S., 2011.The information content of the S&P 500 index and\nVIX options on the dynamics of the S&P 500 index. Journal of Futures Markets, Vol. 31, No. 12,\n1170–1201.\nConrad J., Dittmar R.F., Ghysels E., 2013. Ex Ante Skewness and Expected Stock Returns. Journal of\nFinance Vol. 68, No. 1.\nCordisa S.A., Kirby C., 2014. Discrete stochastic autoregressive volatility. Journal of Banking &\nFinance 43, 160–178.\nCorsi, F, 2009.A simple approximate long-memory model of realized volatility, Journal of Financial\nEconometrics,Vol.7, Issue 2, 174-196\nDueker M., Neely C.J., 2007. Can Markov switching models predict excess foreign exchange returns?\nJournal of Banking & Finance 31, 279–296.\nFernandesa M.,. Medeirosc M.C., Scharth M., 2014. Modeling and predicting the CBOE market\nvolatility index. Journal of Banking & Finance 40, 1–10.\nGatheral, 2008. Consistent Modeling of SPX and VIX options.\nGray S.F, 1996. Modeling the conditional distribution of interest rates as a regime-switching process.\nJournal of Financial Economics 42, 27 - 62.\nHamilton J.D., 1989. A new approach to the economic analysis of nonstationary time series and the\nbusiness cycle. Econometrica Vol. 57, No. 2, 357 - 384.\nHamilton J.D., 1990.Analysis of time series subject to changes in regime. Journal of Econometrics 45,\n39-70.\nKanniainena J., Lina B., Yang H., 2014. Estimating and using GARCH models with VIX data for option\nvaluation. Journal of Banking & Finance 43, 200–211.\nKhalifaa A.A.A, Hammoudehb S., Otranto E., 2014. Patterns of volatility transmissions within regime\nswitching across GCC and global markets. International Review of Economics and Finance 29,\n512–524.\nKim C.J, 1994. Dynamic linear models with Markov-switching. Journal of Econometrics 60, l-22.\nLin Y.N., 2013. VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility\nderivatives valuation. Journal of Banking & Finance 37, 4432–4446.\nLiua X., Margaritisb D., Wang P., 2012. Stock market volatility and equity returns: Evidence from a\ntwo-state Markov-switching model with regressors. Journal of Empirical Finance 19, 483–496.\nMiaoa W.C., Wub C.C., Su Y.K., 2013. Regime-switching in volatility and correlation structure using\nrange-based models with Markov-switching. Economic Modelling 31, 87–93.\nNeumanna M., Skiadopoulos G., 2013.Predictable dynamics in higher order risk-neutral\nmoments:evidence from the S&P 500 options. Journal of Financial and Quantitative Analysis, Vol.\n48, Issue 03, 947 - 977.\nOnan M., Salih A., Burze Yasar, 2014. Impact of macroeconomic announcements on implied volatility\nslope of SPX options and VIX. Finance Research Letters 11, 454–462.\nPan Q., Li Y., 2013. Testing volatility persistence on Markov switching stochastic volatility models.\nEconomic Modelling 35, 45–50.\nPatrick S., Stewart M., 2002. Risk-neutral skewness: evidence from stock options. Journal of Financial\n& Quantitative Analysis, Vol. 37, 471.\nRaggia D., Bordignon S., 2012. Long memory and nonlinearities in realized volatility: A Markov\nswitching approach. Computational Statistics and Data Analysis 56, 3730–3742.\nRaggia, Bordignon, 2012. Long memory and nonlinearities in realized volatility: A Markov switching\napproach. Computational Statistics & Data Analysis,Vol. 56, Issue 11, Pages 3730–3742\nRossia A., Giampiero, 2006. Volatility estimation via hidden Markov models. Journal of Empirical\nFinance 13, 203– 230.\nZhou Y., 2014. Modeling the joint dynamics of risk-neutral stock index and bond yield volatilities.\nJournal of Banking & Finance 38, 216–228zh_TW