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題名 波動自我復歸特性對股價指數選擇權評價重要嗎?
Is Mean Reversion Feature of Volatility Important to Stock Index Option?
作者 湯亞蒨
貢獻者 杜化宇
湯亞蒨
關鍵詞 台指選擇權
條件波動度
Regime-Switching
Dispersion
GRS-GARCH
日期 2009
上傳時間 8-Dec-2010 01:54:27 (UTC+8)
摘要 過去文獻在探究股市報酬率波動行為時,多採用GARCH/ARCH等傳統時間序列模型,但這些模型不能解決波動度的高持續性(persistence)。本文以Gray(1996)提出的一般化狀態轉換模型(GRS-GARCH)為基礎並加入Dueker(1997)所提出的Dispersion設定,建立GRS-GARCH-K以及GRS-GRACH-DF模型來預測股市報酬率波動行為。GRS-GARCH-K模型設定最大的優點是加入Student’s t分配之自由度可隨狀態轉換,使峰態亦可隨狀態轉換,另外GRS-GRACH-DF模型除了擁有GRS-GARCH-K的特性外,還擁有均數復歸的特色。本文以單一狀態下的GARCH-N、GARCH-t模型,以及雙狀態下的GRS-GARCH、GRS-GARCH-K以及GRS-GARCH-DF模型做研究,並以台灣股價加權股價指數為研究樣本,探討並預測股價日報酬率的波動度,最後將波動度代入Black-Scholes選擇權訂價模型,探討模型之其評價效果。
研究顯示,在樣本內以AIC和SBC檢定法則下,GRS-GARCH-DF有最好的配適能力,樣本外的預測能力在MAE、MASE、MAPE三種誤差比較法下,GRS-GARCH-DF相較於GARCH-N、GARCH-t、GRS-GARCH和GRS-GARCH-K四種模型,在訂價方面與市場價格誤差最小,並以DM檢定法證實其統計上的顯著性。因此擁有均數復歸特色的GRS-GARCH-DF在波動度的估計上相較於其他模型來的優異。
參考文獻 一、 中文部分
1. 鄭亦妏,“在Black-Scholes評價模型下台指選擇權最適波動估計方法之研究”, 淡江大學管理科學研究所碩士論文,民國九十一年。
2. 黎明淵, “馬可夫轉換模型應用性與合用性探討”,國立政治大學國際貿易學系博士論文,民國八十九年。
二、英文部分
1. Akgiray, V., (1989) “Conditional Heteroskedasticity in Time Series of Stock Returns: Evidence and Forecasts”, Journal of Business, Vol.62, 55-80.
2. Black, F., (1976) “The pricing of commodity contracts”, Journal of Financial Economics, Vol.3, 167-179.
3. Black, F. and M. Scholes, (1973) “The pricing of options and corporate liabilities”, Journal of Political Economy, Vol.81, 637-659.
4. Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroscedasticity”, Journal of Econometrics, Vol. 31, 307-327.
5. Bollerslev, T., (1987) “A Conditional Heteroscedastic Time Series Model for Speculative Prices and Rates of Return”, Review of Economics and Statistics, Vol. 69, 542-547.
6. Bondarenko, O., (2003) “Why Are Put Options So Expensive?”, Working Paper.
7. Cassuto, A. E., (1995) “Non-Normal Error Patterns : How to Handle Them”, The Journal of Business Forecasting : Methods and System,14, 15-16.
8. Chu, Shin-Herng, and Steven Freund, (1996) “Volatiltiy Estimation for Stock Index Options: A GARCH Approach”, The Quarterly Review of Economics and Finance, Vol.36, 431-450.
9. Day, T. E., and C. M. Lewis, (1998) “The Behavior of the Volatility implicit in the prices of stock index options”, Journal of Financial Economics, 103-122.
10. Diebold, F. X., (1986) “Modeling the Persistence of Conditional Varaince: A Comment”, Journal of the Royal Statistical Society, B39, 1-38.
11. Diebold, F. X. and R.S. Mariano, (1995) “Comparing Predictive accuracy”, Journal of Business and Economic Statistics, Vol.13, 253-263.
12. Ding Zhuanxin, C.W.J. Granger, and R. Engle, (1993) “A Long Memory Property of Stock Market Returns and a New Model”, Journal of Empirical Finance, Vol.1, 83-106.
13. Dueker, Michael J., (1997) “Markov Switching in GARCH Processes and Mean Reverting Stock Market Volatility”, Journal of Business and Economic Statistics, Vol. 15, 26-34.
14. Duan, J. C., and H. Zhang,(2001) “Pricing Hang Seng Index Options around the Asian Financial Crisis-A GARCH Approach”, Journal of Banking and Finance, 1989-2014.
15. Engle, R., (1982) “Autoregressive Conditional Heteroscedasticity with Estimates of Variance of UK Inflation”, Econometrica, Vol. 50, 987-1008.
16. Engle, R. and T. Bollerslev, (1986) “Modeling the Persistence of Conditional Variance”, Econometric Reviews, Vol. 5, 1-50.
17. Fama, E. F., (1965) “The Behavior of Stock Market Prices”, Journal of Business, Vol.38, 34-105.
18. French, K. R., G. W. Schwert, R. F. Stambaugh, (1987) “Expected Stock Returns and Volatility”, Journal of Financial Economics, Vol.19, 3-29.
19. Glosten Lawrence R., Ravi Jagannatha and David E. Runkle, (1993) “On the Relation between the Expected Value and the Volatility of Nominal Excess Return on Stocks”, Journal of Finance, Vol.48, No.5, 1779-1801.
20. Goldfeld, S. M., and R. E. Quandt, (1973) “A Markov Model for Switching Regerssion”, Journal of Econometrics, Vol.1, 3-16.
21. Gwilym, O. A., (2001) “Forecasting volatility for options pricing for the U.K. stock market”, Journal of Financial Management and Analysis, Vol.14, 55-62.
22. Gray, S. F., (1996) “Modeling the conditional distribution of interest rates as a regime-switching process”, Journal of Financial Economics, Vol. 42, 27- 62.
23. Hamilton, J. D. and R. Susmel, (1994) “Autoregressive Conditional Heteroskedasticity and Change in Regime”, Journal of Econometrics, Vol.64, 307-33.
24. Hansen, B. E. (1996) “Erratum: the likelihood ratio test under non-standard conditions: testing the Markov switching model of GNP”, Journal of Applied Econometrics, Vol. 11, 195-198.
25. Harvey D, Leybourne S, Newbold P. (1997) “Testing the equality of prediction mean squared errors”, International Journal of Forecasting,Vol.13, 282–291.
26. Klaassen, F., (2002) “Improving GARCH Volatility Forecasts with Regime-. Switching GARCH”, Empirical Economics, Vol. 27, 363-394.
27. Karadag, Mehmet Ali,(2008)“Analysis of Turkish Sock Market with Markov Regime Switching Volatility Models”, a thesis submitted to the graduate school of applied mathematics of the Middle East Technical University.
28. Latane, H., and R. Rendleman, (1976) “Standard Deviation of Stock Price Ratios Implied in Option Prices”, Journal of Finance, Vol.31, 369-381.
29. Mandelbrot, B., (1963) “The Variation of Certain Speculative Prices”, Journal of Business,Vol.36, 294-419.
30. Marcucci, Juri, (2005) “Forecasting Stock Market Volatility with Regime-Switching GARCH Models”, Studies in Nonlinear Dynamics & Econometrics, Vol. 9, 1-53.
31. Mikosch, T., and C. Starica, (2004) “Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects”, Review of Economics and Statistics, Vol.86, 378-390.
32. Morgan, I.G., (1976) “Stock Prices and Heteroskedasticity”, The Journal of
Business, Vol. 49, 496-508.
33. Nelson, D. B., (1991) “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, Vol.59, 347-370.
34. Pagan, A., (1996) “The Econometrics of Financial Markets”, Journal of Empirical Finance, Vol.3, 15-102.
35. Quandt, R. E., (1972) “A New Approach to Estimating Switching Regressions”, Journal of American Statistical Association,Vol.67, 306-310.
描述 碩士
國立政治大學
財務管理研究所
97357025
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097357025
資料類型 thesis
dc.contributor.advisor 杜化宇zh_TW
dc.contributor.author (Authors) 湯亞蒨zh_TW
dc.creator (作者) 湯亞蒨zh_TW
dc.date (日期) 2009en_US
dc.date.accessioned 8-Dec-2010 01:54:27 (UTC+8)-
dc.date.available 8-Dec-2010 01:54:27 (UTC+8)-
dc.date.issued (上傳時間) 8-Dec-2010 01:54:27 (UTC+8)-
dc.identifier (Other Identifiers) G0097357025en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/48969-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 財務管理研究所zh_TW
dc.description (描述) 97357025zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 過去文獻在探究股市報酬率波動行為時,多採用GARCH/ARCH等傳統時間序列模型,但這些模型不能解決波動度的高持續性(persistence)。本文以Gray(1996)提出的一般化狀態轉換模型(GRS-GARCH)為基礎並加入Dueker(1997)所提出的Dispersion設定,建立GRS-GARCH-K以及GRS-GRACH-DF模型來預測股市報酬率波動行為。GRS-GARCH-K模型設定最大的優點是加入Student’s t分配之自由度可隨狀態轉換,使峰態亦可隨狀態轉換,另外GRS-GRACH-DF模型除了擁有GRS-GARCH-K的特性外,還擁有均數復歸的特色。本文以單一狀態下的GARCH-N、GARCH-t模型,以及雙狀態下的GRS-GARCH、GRS-GARCH-K以及GRS-GARCH-DF模型做研究,並以台灣股價加權股價指數為研究樣本,探討並預測股價日報酬率的波動度,最後將波動度代入Black-Scholes選擇權訂價模型,探討模型之其評價效果。
研究顯示,在樣本內以AIC和SBC檢定法則下,GRS-GARCH-DF有最好的配適能力,樣本外的預測能力在MAE、MASE、MAPE三種誤差比較法下,GRS-GARCH-DF相較於GARCH-N、GARCH-t、GRS-GARCH和GRS-GARCH-K四種模型,在訂價方面與市場價格誤差最小,並以DM檢定法證實其統計上的顯著性。因此擁有均數復歸特色的GRS-GARCH-DF在波動度的估計上相較於其他模型來的優異。
zh_TW
dc.description.tableofcontents 第壹章 緒論
第一節 研究背景與動機……………………………………………………1.
第二節 研究目的……………………………………………………………3.
第三節 研究架構……………………………………………………………4.
第四節 研究流程圖…………………………………………………………5.
第貳章 文獻回顧與探討
第一節 波動度理論模型與文獻回顧………………………………………6.
第二節 狀態轉換之相關文獻………………………………………………9.
第三節 選擇權之相關介紹與文獻…………………………………………12.
第參章 研究方法
第一節 本文使用模型介紹…………………………………………………15.
第二節 模型配適度檢定……………………………………………………22.
第三節 模型預測與預測績效之檢定………………………………………23.
第肆章 實證結果與分析
第一節 樣本資料介紹與資料處理方法……………………………………27.
第二節 各種模型之探討與比較……………………………………………31.
第三節 樣本內模型配適度結果與分析……………………………………36.
第四節 樣本外預測結果與分析……………………………………………39.
第伍章 研究結論與建議……………………………………………..45.
附錄……………………………………………………………………47.
參考文獻………………………………………………………………49.
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097357025en_US
dc.subject (關鍵詞) 台指選擇權zh_TW
dc.subject (關鍵詞) 條件波動度zh_TW
dc.subject (關鍵詞) Regime-Switchingen_US
dc.subject (關鍵詞) Dispersionen_US
dc.subject (關鍵詞) GRS-GARCHen_US
dc.title (題名) 波動自我復歸特性對股價指數選擇權評價重要嗎?zh_TW
dc.title (題名) Is Mean Reversion Feature of Volatility Important to Stock Index Option?en_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 一、 中文部分zh_TW
dc.relation.reference (參考文獻) 1. 鄭亦妏,“在Black-Scholes評價模型下台指選擇權最適波動估計方法之研究”, 淡江大學管理科學研究所碩士論文,民國九十一年。zh_TW
dc.relation.reference (參考文獻) 2. 黎明淵, “馬可夫轉換模型應用性與合用性探討”,國立政治大學國際貿易學系博士論文,民國八十九年。zh_TW
dc.relation.reference (參考文獻) 二、英文部分zh_TW
dc.relation.reference (參考文獻) 1. Akgiray, V., (1989) “Conditional Heteroskedasticity in Time Series of Stock Returns: Evidence and Forecasts”, Journal of Business, Vol.62, 55-80.zh_TW
dc.relation.reference (參考文獻) 2. Black, F., (1976) “The pricing of commodity contracts”, Journal of Financial Economics, Vol.3, 167-179.zh_TW
dc.relation.reference (參考文獻) 3. Black, F. and M. Scholes, (1973) “The pricing of options and corporate liabilities”, Journal of Political Economy, Vol.81, 637-659.zh_TW
dc.relation.reference (參考文獻) 4. Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroscedasticity”, Journal of Econometrics, Vol. 31, 307-327.zh_TW
dc.relation.reference (參考文獻) 5. Bollerslev, T., (1987) “A Conditional Heteroscedastic Time Series Model for Speculative Prices and Rates of Return”, Review of Economics and Statistics, Vol. 69, 542-547.zh_TW
dc.relation.reference (參考文獻) 6. Bondarenko, O., (2003) “Why Are Put Options So Expensive?”, Working Paper.zh_TW
dc.relation.reference (參考文獻) 7. Cassuto, A. E., (1995) “Non-Normal Error Patterns : How to Handle Them”, The Journal of Business Forecasting : Methods and System,14, 15-16.zh_TW
dc.relation.reference (參考文獻) 8. Chu, Shin-Herng, and Steven Freund, (1996) “Volatiltiy Estimation for Stock Index Options: A GARCH Approach”, The Quarterly Review of Economics and Finance, Vol.36, 431-450.zh_TW
dc.relation.reference (參考文獻) 9. Day, T. E., and C. M. Lewis, (1998) “The Behavior of the Volatility implicit in the prices of stock index options”, Journal of Financial Economics, 103-122.zh_TW
dc.relation.reference (參考文獻) 10. Diebold, F. X., (1986) “Modeling the Persistence of Conditional Varaince: A Comment”, Journal of the Royal Statistical Society, B39, 1-38.zh_TW
dc.relation.reference (參考文獻) 11. Diebold, F. X. and R.S. Mariano, (1995) “Comparing Predictive accuracy”, Journal of Business and Economic Statistics, Vol.13, 253-263.zh_TW
dc.relation.reference (參考文獻) 12. Ding Zhuanxin, C.W.J. Granger, and R. Engle, (1993) “A Long Memory Property of Stock Market Returns and a New Model”, Journal of Empirical Finance, Vol.1, 83-106.zh_TW
dc.relation.reference (參考文獻) 13. Dueker, Michael J., (1997) “Markov Switching in GARCH Processes and Mean Reverting Stock Market Volatility”, Journal of Business and Economic Statistics, Vol. 15, 26-34.zh_TW
dc.relation.reference (參考文獻) 14. Duan, J. C., and H. Zhang,(2001) “Pricing Hang Seng Index Options around the Asian Financial Crisis-A GARCH Approach”, Journal of Banking and Finance, 1989-2014.zh_TW
dc.relation.reference (參考文獻) 15. Engle, R., (1982) “Autoregressive Conditional Heteroscedasticity with Estimates of Variance of UK Inflation”, Econometrica, Vol. 50, 987-1008.zh_TW
dc.relation.reference (參考文獻) 16. Engle, R. and T. Bollerslev, (1986) “Modeling the Persistence of Conditional Variance”, Econometric Reviews, Vol. 5, 1-50.zh_TW
dc.relation.reference (參考文獻) 17. Fama, E. F., (1965) “The Behavior of Stock Market Prices”, Journal of Business, Vol.38, 34-105.zh_TW
dc.relation.reference (參考文獻) 18. French, K. R., G. W. Schwert, R. F. Stambaugh, (1987) “Expected Stock Returns and Volatility”, Journal of Financial Economics, Vol.19, 3-29.zh_TW
dc.relation.reference (參考文獻) 19. Glosten Lawrence R., Ravi Jagannatha and David E. Runkle, (1993) “On the Relation between the Expected Value and the Volatility of Nominal Excess Return on Stocks”, Journal of Finance, Vol.48, No.5, 1779-1801.zh_TW
dc.relation.reference (參考文獻) 20. Goldfeld, S. M., and R. E. Quandt, (1973) “A Markov Model for Switching Regerssion”, Journal of Econometrics, Vol.1, 3-16.zh_TW
dc.relation.reference (參考文獻) 21. Gwilym, O. A., (2001) “Forecasting volatility for options pricing for the U.K. stock market”, Journal of Financial Management and Analysis, Vol.14, 55-62.zh_TW
dc.relation.reference (參考文獻) 22. Gray, S. F., (1996) “Modeling the conditional distribution of interest rates as a regime-switching process”, Journal of Financial Economics, Vol. 42, 27- 62.zh_TW
dc.relation.reference (參考文獻) 23. Hamilton, J. D. and R. Susmel, (1994) “Autoregressive Conditional Heteroskedasticity and Change in Regime”, Journal of Econometrics, Vol.64, 307-33.zh_TW
dc.relation.reference (參考文獻) 24. Hansen, B. E. (1996) “Erratum: the likelihood ratio test under non-standard conditions: testing the Markov switching model of GNP”, Journal of Applied Econometrics, Vol. 11, 195-198.zh_TW
dc.relation.reference (參考文獻) 25. Harvey D, Leybourne S, Newbold P. (1997) “Testing the equality of prediction mean squared errors”, International Journal of Forecasting,Vol.13, 282–291.zh_TW
dc.relation.reference (參考文獻) 26. Klaassen, F., (2002) “Improving GARCH Volatility Forecasts with Regime-. Switching GARCH”, Empirical Economics, Vol. 27, 363-394.zh_TW
dc.relation.reference (參考文獻) 27. Karadag, Mehmet Ali,(2008)“Analysis of Turkish Sock Market with Markov Regime Switching Volatility Models”, a thesis submitted to the graduate school of applied mathematics of the Middle East Technical University.zh_TW
dc.relation.reference (參考文獻) 28. Latane, H., and R. Rendleman, (1976) “Standard Deviation of Stock Price Ratios Implied in Option Prices”, Journal of Finance, Vol.31, 369-381.zh_TW
dc.relation.reference (參考文獻) 29. Mandelbrot, B., (1963) “The Variation of Certain Speculative Prices”, Journal of Business,Vol.36, 294-419.zh_TW
dc.relation.reference (參考文獻) 30. Marcucci, Juri, (2005) “Forecasting Stock Market Volatility with Regime-Switching GARCH Models”, Studies in Nonlinear Dynamics & Econometrics, Vol. 9, 1-53.zh_TW
dc.relation.reference (參考文獻) 31. Mikosch, T., and C. Starica, (2004) “Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects”, Review of Economics and Statistics, Vol.86, 378-390.zh_TW
dc.relation.reference (參考文獻) 32. Morgan, I.G., (1976) “Stock Prices and Heteroskedasticity”, The Journal ofzh_TW
dc.relation.reference (參考文獻) Business, Vol. 49, 496-508.zh_TW
dc.relation.reference (參考文獻) 33. Nelson, D. B., (1991) “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, Vol.59, 347-370.zh_TW
dc.relation.reference (參考文獻) 34. Pagan, A., (1996) “The Econometrics of Financial Markets”, Journal of Empirical Finance, Vol.3, 15-102.zh_TW
dc.relation.reference (參考文獻) 35. Quandt, R. E., (1972) “A New Approach to Estimating Switching Regressions”, Journal of American Statistical Association,Vol.67, 306-310.zh_TW