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題名 以變異數比率法檢定指數選擇權之買賣權平價理論——馬可夫狀態轉換模型之應用
作者 秦秀琪
貢獻者 杜化宇
none
秦秀琪
關鍵詞 馬可夫狀態轉換模型
買賣權平價理論
變異數比率檢定法
股利不勸定性
Markov Regime Switching Model
Put-Call Parity
Variance Ratio Test
Dividend Uncertainty
日期 2002
上傳時間 17-Sep-2009 19:10:05 (UTC+8)
摘要 本研究目的在於探討Put-Call Parity(PCP)所隱含的買權、賣權與標的資產間的價格變動關係。藉由探討PCP偏差程度的動態行為,推論若PCP的偏差為隨機漫步過程,則無法達到長期穩定,隱含PCP的廣義關係無法成立;反之,若PCP的偏差具有回歸平均特性,表示長期會達到穩定狀態,則PCP的廣義關係成立。
在研究方法上本文以變異數比率法檢定指數選擇權的PCP偏差是否為隨機漫步過程,採用隱含利率和實際無風險利率的差代表PCP的偏差程度,利用馬可夫轉換模型描繪PCP偏差的動態行為,並使用Gibbs Sampling演算法說明參數的不確定性。
本文以S&P500和DAX為研究標的,並探討股利不確定性是否影響PCP廣義關係,得到下列結論:
1、 對於S&P 500指數選擇權而言,不論是以日資料或週資料估計VR,S&P 500的PCP偏差都無法提供回歸平均的證據,隱含S&P 500的PCP廣義關係無法成立。
2、 對於DAX指數選擇權而言,檢定日資料的結果發現,DAX之PCP偏差在長期時(40~50日)有明顯的回歸平均的證據;而在檢定週資料時,使用原始資料法在90%信心水準下,不論取任何lag都可拒絕虛無假設,使用標準化資料則無法提供明顯的回歸平均證據。
3、 比較S&P 500和DAX,檢定日資料與週資料的結果都發現,DAX的p-value都比S&P 500小,並且S&P 500的PCP偏差都無法提供回歸平均的證據,而DAX有明顯回歸平均現象,隱含在消除股利的不確定性後,指數選擇權PCP的廣義關係式成立之證據較強烈。
參考文獻 Albert, J. H., and Chib, S. (1993) “Bayesian Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts.” Journal of Business and Economic Statistics, 11(1), 1-15.
Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroscedasticity.” Journal of Econometrics, 31, 307-327.
Campbell, J. Y., Lo, A. W. and MacKinlay A. C. (1997) The Econometrics of Financial Markets., Princeton University Press
Casella, G. and George, E. I. (1993) “Explaining the Gibbs Sampler.” The American Statistician, 46(3), 167-174.
Chib, S. and Greenberg, E. (1996) “Markov Chain Monte Carlo Simulation Methods in Econometrics.” Econometric Theory, 12, 409-431.
Cochrane, J. H. (1988) “How big is the random walk in GNP?” Journal of Political Economy, 96, 893-920.
Dickey, D. A., and Fuller, W. A. (1979) “Distribution of the Estimates for Autoregressive Time Series with a Unit Root.” Journal of the American Statistical Association, 427-431.
Draper, P. and Fung, J. K. W. (2002) “A Study of Arbitrage Efficiency Between the FTSE-100 Index Futures and Options Contracts.” Journal of Futures Markets, 22(1), 31-58.
Enders, W. (1995) Applied Econometric Time Series. Wiley
Engle, R. F. (1982) “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica, 50, 987-1007.
de Roon, F. and Chris Veld, (1996) “Put-Call Parities and the Value of Early Exercise for Put Options on a Performance Index.” Journal of Futures Markets, 16(1), 71-80.
Franses, P. H. and Dijk, D. V. (2000) Nonlinear Time Series Models in Empirical Finance. Cambridge University Press
Finucane, T. J. (199) “Put-Call Parity and Expected Returns.” Journal of Financial Quantitative Analysis, 26(4), 445-457.
Fung, J. K. W. and Chan, K. C. (1994) “On the Arbitrage-free Pricing Relationship Between Index Futures and Index Options: A note.” Journal of Futures Markets, 14(8), 957–962.
Gefland, A. E. and Smith, A. F. M. (1990) “Sampling Based Approaches to Calculating Marginal Densities.” Journal of American Statistical Association, 85, 398-409.
Gefland, A. E., Smith, A. F. M. and Lee, T. M. (1990) “Bayesian Analysis of Constrained Parameters and Truncated Data Problems Using Gibbs Sampling.” Journal of American Statistical Association, 87, 523-532.
Geman, S. and Geman, D. (1984) “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
Goldfeld, S. M. and Quandt, R. E. (1973) “A Markov Model for Switching Regressions.” Journal of Econometrics, 1, 3-16.
Graflund, Andreas (2002) “A Bayesian Inference Approach to Testing Mean Reversion in the Swedish Stock Market.” Department of Economics, Lund University
Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press.
Hamilton, J. D. (1989) “A new Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica, 57(2), 357-384.
Hamilton, J. D. (1990) “Analysis of Time Series subject to Changes in Regime.” Journal of Econometrics, 45, 39-70.
Hamilton, J. D. (1991) “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions.” Journal of Business and Economic Statistics, 19, 23-39.
Hamilton, J. D. and Susmel, R. (1994) “Autoregressive Conditional Heteroskedasticity and Changes in Regime.” Journal of Econometrics, 64, 307-333.
Hull, J. C. (2000) Options, Futures, & Other Derivatives 4th ed. Prentice Hall
Kamara, A. and Miller, T. W. (1995) “Daily and Intradaily Tests of European Put-Call Parity.” Journal of Financial and Quantitative Analysis, 30(4), 519-539.
Kim, C. J. and Nelson, C. R. (1999) State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications., MIT Press
Kim, C. J. and Nelson, C. R. (1998) “Business Cycle Turning Points, a New Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model with Regime Switching.” The Review of Economics and Statistics, 80(2), 188-201.
Kim, C. J. and Nelson, C. R. (1998) “Testing for mean Reversion in heteroskedastic data II: Autocorrelation Tests based on Gibbs-Sampling-Augmented Randomization.” Journal of Empirical Finance, 5(2), 385-396.
Kim, C. J., Nelson, C. R. and Startz, R. (1991) “Mean reversion in stock prices? A Reappraisal of the Empirical Evidence” Review of Economic Studies, 58, 515-528.
Kim, C. J., Nelson, C. R. and Startz, R. (1998) “Testing for mean reversion in heteroskedastic data based on Gibbs-sampling-augmented randomization” Journal of Empirical Finance, 5(2), 131-154.
Kuan, C. M. “Lecture on the Markov Switching Model.” Institute of Economics Academia Sinica.
Lo, A. W. and MacKinlay, A. C. (1988) “Stock Market Prices do not follow Random Walks: Evidence from a Simple Specification Test.” The Review of Financial Studies, 1, 41-66.
Lo, A. W. and MacKinlay, A. C. (1989) “The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation.” Journal of Econometrics, 45, 203-238.
Malliaropulos, D. and Priestley, R. (1999) “Mean Reversion in Southeast Asian Stock Markets.” Journal of Empirical Finance, 6, 355-384.
Neal, R. (1996) “Direct Tests of Index Arbitrage Models.” Journal of Financial and Quantitative Analysis, 31(4), 541-562.
Noreen, E. W. (1989) Computer-Intensive Methods for Testing Hypotheses: An Introduction. Wiley
Poterba, J. M. and Summers, L. H. (1988) “Mean Reversion in Stock Prices: Evidence and Implications.” Journal of Financial Economics, 22(1), 27-60.
Stoll, H. R. (1969) “The Relationship between Put and Call Prices.” Journal of Finance, 24, 810-822.
Tsay, R. S. (2002) Analysis of Financial Time Series. Wiely
Zivney, T. L. (1991) “The Value of Early Exercise in Option Prices: An Empirical Investigation.” Journal of Financial and Quantitative Analysis, 26(1), 129-138.
描述 碩士
國立政治大學
財務管理研究所
90357005
91
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0090357005
資料類型 thesis
dc.contributor.advisor 杜化宇zh_TW
dc.contributor.advisor noneen_US
dc.contributor.author (Authors) 秦秀琪zh_TW
dc.creator (作者) 秦秀琪zh_TW
dc.date (日期) 2002en_US
dc.date.accessioned 17-Sep-2009 19:10:05 (UTC+8)-
dc.date.available 17-Sep-2009 19:10:05 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 19:10:05 (UTC+8)-
dc.identifier (Other Identifiers) G0090357005en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/34032-
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) 90357005zh_TW
dc.description (描述) 91zh_TW
dc.description.abstract (摘要) 本研究目的在於探討Put-Call Parity(PCP)所隱含的買權、賣權與標的資產間的價格變動關係。藉由探討PCP偏差程度的動態行為,推論若PCP的偏差為隨機漫步過程,則無法達到長期穩定,隱含PCP的廣義關係無法成立;反之,若PCP的偏差具有回歸平均特性,表示長期會達到穩定狀態,則PCP的廣義關係成立。
在研究方法上本文以變異數比率法檢定指數選擇權的PCP偏差是否為隨機漫步過程,採用隱含利率和實際無風險利率的差代表PCP的偏差程度,利用馬可夫轉換模型描繪PCP偏差的動態行為,並使用Gibbs Sampling演算法說明參數的不確定性。
本文以S&P500和DAX為研究標的,並探討股利不確定性是否影響PCP廣義關係,得到下列結論:
1、 對於S&P 500指數選擇權而言,不論是以日資料或週資料估計VR,S&P 500的PCP偏差都無法提供回歸平均的證據,隱含S&P 500的PCP廣義關係無法成立。
2、 對於DAX指數選擇權而言,檢定日資料的結果發現,DAX之PCP偏差在長期時(40~50日)有明顯的回歸平均的證據;而在檢定週資料時,使用原始資料法在90%信心水準下,不論取任何lag都可拒絕虛無假設,使用標準化資料則無法提供明顯的回歸平均證據。
3、 比較S&P 500和DAX,檢定日資料與週資料的結果都發現,DAX的p-value都比S&P 500小,並且S&P 500的PCP偏差都無法提供回歸平均的證據,而DAX有明顯回歸平均現象,隱含在消除股利的不確定性後,指數選擇權PCP的廣義關係式成立之證據較強烈。
zh_TW
dc.description.tableofcontents 第一章 緒論 1
第一節 研究動機與目的 1
第二節 研究方法 2
第三節 研究架構 3
第二章 理論基礎與文獻探討 6
第一節 變異數比率檢定(Variance Ratio Test) 6
第二節 VR的同質性變異與異質性變異的樣本分配 8
第三章 研究方法 18
第一節 歐式指數選擇權之Put-Call Parity 18
第二節 以馬可夫轉換模型描繪PCP偏差的動態行為 24
第三節 估計馬可夫轉換模型的參數及狀態變數 28
第四節 估計Variance Ratios的樣本分配 38
第四章 實證結果 42
第一節 研究標的 42
第二節 資料選取 44
第三節 使用馬可夫轉換模型的適當性 48
第四節 Variance Ratio檢定結果 58
第五章 總結與結論 71
第一節 總結 71
第二節 結論 73
zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0090357005en_US
dc.subject (關鍵詞) 馬可夫狀態轉換模型zh_TW
dc.subject (關鍵詞) 買賣權平價理論zh_TW
dc.subject (關鍵詞) 變異數比率檢定法zh_TW
dc.subject (關鍵詞) 股利不勸定性zh_TW
dc.subject (關鍵詞) Markov Regime Switching Modelen_US
dc.subject (關鍵詞) Put-Call Parityen_US
dc.subject (關鍵詞) Variance Ratio Testen_US
dc.subject (關鍵詞) Dividend Uncertaintyen_US
dc.title (題名) 以變異數比率法檢定指數選擇權之買賣權平價理論——馬可夫狀態轉換模型之應用zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Albert, J. H., and Chib, S. (1993) “Bayesian Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts.” Journal of Business and Economic Statistics, 11(1), 1-15.zh_TW
dc.relation.reference (參考文獻) Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroscedasticity.” Journal of Econometrics, 31, 307-327.zh_TW
dc.relation.reference (參考文獻) Campbell, J. Y., Lo, A. W. and MacKinlay A. C. (1997) The Econometrics of Financial Markets., Princeton University Presszh_TW
dc.relation.reference (參考文獻) Casella, G. and George, E. I. (1993) “Explaining the Gibbs Sampler.” The American Statistician, 46(3), 167-174.zh_TW
dc.relation.reference (參考文獻) Chib, S. and Greenberg, E. (1996) “Markov Chain Monte Carlo Simulation Methods in Econometrics.” Econometric Theory, 12, 409-431.zh_TW
dc.relation.reference (參考文獻) Cochrane, J. H. (1988) “How big is the random walk in GNP?” Journal of Political Economy, 96, 893-920.zh_TW
dc.relation.reference (參考文獻) Dickey, D. A., and Fuller, W. A. (1979) “Distribution of the Estimates for Autoregressive Time Series with a Unit Root.” Journal of the American Statistical Association, 427-431.zh_TW
dc.relation.reference (參考文獻) Draper, P. and Fung, J. K. W. (2002) “A Study of Arbitrage Efficiency Between the FTSE-100 Index Futures and Options Contracts.” Journal of Futures Markets, 22(1), 31-58.zh_TW
dc.relation.reference (參考文獻) Enders, W. (1995) Applied Econometric Time Series. Wileyzh_TW
dc.relation.reference (參考文獻) Engle, R. F. (1982) “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica, 50, 987-1007.zh_TW
dc.relation.reference (參考文獻) de Roon, F. and Chris Veld, (1996) “Put-Call Parities and the Value of Early Exercise for Put Options on a Performance Index.” Journal of Futures Markets, 16(1), 71-80.zh_TW
dc.relation.reference (參考文獻) Franses, P. H. and Dijk, D. V. (2000) Nonlinear Time Series Models in Empirical Finance. Cambridge University Presszh_TW
dc.relation.reference (參考文獻) Finucane, T. J. (199) “Put-Call Parity and Expected Returns.” Journal of Financial Quantitative Analysis, 26(4), 445-457.zh_TW
dc.relation.reference (參考文獻) Fung, J. K. W. and Chan, K. C. (1994) “On the Arbitrage-free Pricing Relationship Between Index Futures and Index Options: A note.” Journal of Futures Markets, 14(8), 957–962.zh_TW
dc.relation.reference (參考文獻) Gefland, A. E. and Smith, A. F. M. (1990) “Sampling Based Approaches to Calculating Marginal Densities.” Journal of American Statistical Association, 85, 398-409.zh_TW
dc.relation.reference (參考文獻) Gefland, A. E., Smith, A. F. M. and Lee, T. M. (1990) “Bayesian Analysis of Constrained Parameters and Truncated Data Problems Using Gibbs Sampling.” Journal of American Statistical Association, 87, 523-532.zh_TW
dc.relation.reference (參考文獻) Geman, S. and Geman, D. (1984) “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.zh_TW
dc.relation.reference (參考文獻) Goldfeld, S. M. and Quandt, R. E. (1973) “A Markov Model for Switching Regressions.” Journal of Econometrics, 1, 3-16.zh_TW
dc.relation.reference (參考文獻) Graflund, Andreas (2002) “A Bayesian Inference Approach to Testing Mean Reversion in the Swedish Stock Market.” Department of Economics, Lund Universityzh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1989) “A new Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica, 57(2), 357-384.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1990) “Analysis of Time Series subject to Changes in Regime.” Journal of Econometrics, 45, 39-70.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1991) “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions.” Journal of Business and Economic Statistics, 19, 23-39.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. and Susmel, R. (1994) “Autoregressive Conditional Heteroskedasticity and Changes in Regime.” Journal of Econometrics, 64, 307-333.zh_TW
dc.relation.reference (參考文獻) Hull, J. C. (2000) Options, Futures, & Other Derivatives 4th ed. Prentice Hallzh_TW
dc.relation.reference (參考文獻) Kamara, A. and Miller, T. W. (1995) “Daily and Intradaily Tests of European Put-Call Parity.” Journal of Financial and Quantitative Analysis, 30(4), 519-539.zh_TW
dc.relation.reference (參考文獻) Kim, C. J. and Nelson, C. R. (1999) State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications., MIT Presszh_TW
dc.relation.reference (參考文獻) Kim, C. J. and Nelson, C. R. (1998) “Business Cycle Turning Points, a New Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model with Regime Switching.” The Review of Economics and Statistics, 80(2), 188-201.zh_TW
dc.relation.reference (參考文獻) Kim, C. J. and Nelson, C. R. (1998) “Testing for mean Reversion in heteroskedastic data II: Autocorrelation Tests based on Gibbs-Sampling-Augmented Randomization.” Journal of Empirical Finance, 5(2), 385-396.zh_TW
dc.relation.reference (參考文獻) Kim, C. J., Nelson, C. R. and Startz, R. (1991) “Mean reversion in stock prices? A Reappraisal of the Empirical Evidence” Review of Economic Studies, 58, 515-528.zh_TW
dc.relation.reference (參考文獻) Kim, C. J., Nelson, C. R. and Startz, R. (1998) “Testing for mean reversion in heteroskedastic data based on Gibbs-sampling-augmented randomization” Journal of Empirical Finance, 5(2), 131-154.zh_TW
dc.relation.reference (參考文獻) Kuan, C. M. “Lecture on the Markov Switching Model.” Institute of Economics Academia Sinica.zh_TW
dc.relation.reference (參考文獻) Lo, A. W. and MacKinlay, A. C. (1988) “Stock Market Prices do not follow Random Walks: Evidence from a Simple Specification Test.” The Review of Financial Studies, 1, 41-66.zh_TW
dc.relation.reference (參考文獻) Lo, A. W. and MacKinlay, A. C. (1989) “The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation.” Journal of Econometrics, 45, 203-238.zh_TW
dc.relation.reference (參考文獻) Malliaropulos, D. and Priestley, R. (1999) “Mean Reversion in Southeast Asian Stock Markets.” Journal of Empirical Finance, 6, 355-384.zh_TW
dc.relation.reference (參考文獻) Neal, R. (1996) “Direct Tests of Index Arbitrage Models.” Journal of Financial and Quantitative Analysis, 31(4), 541-562.zh_TW
dc.relation.reference (參考文獻) Noreen, E. W. (1989) Computer-Intensive Methods for Testing Hypotheses: An Introduction. Wileyzh_TW
dc.relation.reference (參考文獻) Poterba, J. M. and Summers, L. H. (1988) “Mean Reversion in Stock Prices: Evidence and Implications.” Journal of Financial Economics, 22(1), 27-60.zh_TW
dc.relation.reference (參考文獻) Stoll, H. R. (1969) “The Relationship between Put and Call Prices.” Journal of Finance, 24, 810-822.zh_TW
dc.relation.reference (參考文獻) Tsay, R. S. (2002) Analysis of Financial Time Series. Wielyzh_TW
dc.relation.reference (參考文獻) Zivney, T. L. (1991) “The Value of Early Exercise in Option Prices: An Empirical Investigation.” Journal of Financial and Quantitative Analysis, 26(1), 129-138.zh_TW