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題名 緩長記憶效應下的選擇權評價
作者 彭貴田
貢獻者 郭維裕
彭貴田
關鍵詞 緩長記憶
碎形布朗運動
Hurst 指數
R/S分析
碎形Black-Scholes選擇權評價
日期 2005
上傳時間 17-Sep-2009 18:55:11 (UTC+8)
摘要 傳統效率市場假設股價的波動是隨機的,亦即股價是無法預測。 近來的文獻指出股價的波動是不完全是隨機的,且股價的波動具有緩長記憶(long memory)的特性。在本文中我們以R/S分析發現臺灣股市的Hurst指數為0.68,即具有趨勢持續性(trend persistent)之效果,根據此依特性,我們根據Necula(2002)的研究,來評價台股選擇權,發現此新評價模式產生之價格較接近市場價格。
參考文獻 1. Bachelier, La Th´oerie de la Sp´eculation [Ph.D. thesis in mathematics], (1900), Ann. Sci. Ecole Norm. Super., S´er. 3, 17, 21.
2. Backus, D.K. and S.E. Zin, (1993), “long-memory inflation uncertainty: Evidence from the term structure of interest rates.” Journal of Money, Credit and Banking 25, 681-700.
3. Baillie, R.T., (1996), “Long-memory processes and fractional integration in econometrics.” Journal of Econometrics 73, 5-5
4. Baillie, R.T., C.-F. Chung, and M.A. Tieslau,( 1995), Analyzing inflation by the fractional integrated ARFIMA-GARCH model. Journal of Applied Econometrics 11, 23-40.
5. Beran, J., (1994), “Statistics for Long-Memory Processes.” Chapman & Hall.
6. Black, F., and M. Scholes, (1972) ”The Valuation of Option Contracts and a Test of Market Efficiency,” Journal of Finance, 27 - 2, May, 399 - 418.
7. Black, F., and M. Scholes, (1973) “The pricing of options and corporate liabilities”, Journal of Political Economy , vol.81:3,637-54.
8. Costa R. L. and Vasconcelos G. L. (2003), Physica A 329, 231.
9. Di Matteo T., Aste T., M. Dacorogna M., Physica A 324, 183 (2003); Cond-Mat preprint 0302434, 2003.
10. Diebold, F.X. and G.D. Rudebusch, (1989), “Long-memory and persistence in aggregate output.” Journal of Monetary Economics 24, 189-209.
11. Embrechts, Paul and Makoto Maejima. (2002), “Selfsimilar Processes.” Princeton University Press.
12. Fama E. F. (1965), “Tha Behavior of Stock-Market Prices,” The Journal of Business of the University of Chicago, 38, no.1
13. Fama E. F. (1970), “Efficient capital market: A review”, J. Finance 383-417
14. Fleming, J., (1998), "The quality of market volatility forecasts implied by S&P100 index options prices", Journal of Empirical Finance, vol.5, 317-345.
15. Grant, D., G. Vora, and D. Weeks, (1996), "Simulation and the Early-Exercise Option Problem," Journal of Financial Engineering, vol.5(3), 211-227.
16. Grau-Carles P. (2000), Physica A , 287-396.
17. Harrison, M. and D. Kreps, (1979), “Martingales and Multiperiod Securities Markets”, Journal of Economic Theory, vol.20, 381-408
18. Hassler, U. and J. Wolters, (1995), “Long-memory in inflation rates: International evidence.” Journal of Business and Economic Statistics, vol.13, 37-45.
19. Hu, Y. and Øksendal, B (2000), “Fractional white noise calculus and applications to finance”, Preprint, University of Oslo.
20. Hurst, H. (1951), “Long term storage capacity of reservoirs”, Transactions of the American Society of Civil Engineers. Vol.116, 770-790.
21. Jorion, P., (1995), “Predicting volatility in the foreign exchange market”, Journal of Finance. vol.50, 507-528
22. Lo, A.W., (1991), “Long-term memory in stock market prices.” Econometrica, vol.59, 1279-1313.
23. Mandelbrot B. B., (1963), J. Business(Chicago), vol.36, 394
24. Mandelbrot, B. B. and Hudson, R. L. (2004). “The Behavior of Markets: A Fractal View of Risk, Ruin and Reward.” Basic Books, New York, NY.
25. Mandelbrot, B.B., and H.W. Taylor, (1967), “On the distributions of stock price differences". Operations Research., vol.15, 1057-1062.
26. Mandelbrot B.B. and J. W. Van Ness, (1968), SIAM Review 10, 422-437.
27. Mandelbrot, B.B., (1971),”A Fast Fractional Gaussian Noise Generator”, Water Resources Research, 7, 543-553.
28. Mandelbrot B. B., (1997) “Fractals and scaling in finance” Springer, New York,
29. Mantegna R. and H. E. Stanley, (2000), “An Introduction to Econophysics”,Cambridge Univ. Press, Cambridge.
30. Matacz A., (2000), Int. J. Theor. Appl. Financ. 3, 143-160.
31. Miranda L. C. and R. Riera, (2001), Physica A 297, 509-520.
32. Necula, Ciprian (2002), “Option Pricing in a Fractional Brownian Motion Environment”, Draft, Academy of Economic Studies, Bucharest, Romania.
33. Osborne, M.F.M. (1959), “Brownian Motion in The Stock market.”Operations Research. vol. 7, 145-173.
34. Peng, C.-K., S.V. Buldyrev, S. Havlin, M. Simons, and H.E. Stanley, 1994, Goldberger AL., “Mosaic organization of DNA nucleotides”, Physical Review E49, 1685-1689.
35. Peters E. E.,(1991), “Chaos and order in capital markets”, Wiley, New York.
36. Peters E. E.,(1994), “Fractal Market Analysis: Applying Chaos Theory to Investment and Economics”, Wiley, New York.
37. Razdan, A. (2002)., “Scaling in the Bombay stock exchange index.” ramana-Journal of physics, Vol. 58, No. 3, March 2002, p. 537-544
38. Rydberg, T. (1997), “Why Financial Data are Interesting to Statisticians”, Centre for Analytical Finance, Aarhus UniversityWorking Paper 5.
39. Samuelson, P.A. (1964). “Rational Theory of Warrant Pricing. In The Random character of Stock Market Prices”, Ed. P. Cootner, pp 506-532, Cambridge, MIT Press.
40. Schoutens W., (2003), “L´evy Processes in Finance: Pricing Financial Derivatives”, Wiley.
41. Shea, G.S., (1991), “Uncertainty and implied variance bounds in long-memory models of the interest rate term structure.” Empirical Economics, vol. 16, 287-312.
42. Shiryaev A. N., (1999), “Essentials of Stochastic Finance: Facts, Models,Theory, World Scientific”, Singapore.
43. Teverovsky, V., M.S. Taqqu, and W. Willinger, (1999), “A critical look to Lo’s modified R/S statistics.” Journal of Statistical Planning and Inference, vol. 80, 211-227.
44. Vandewalle N., Ausloos M., (1997), Physica A 246-454.
45. Wiener N., J. (1923), Math. Phys. Math. 2, 131.
描述 碩士
國立政治大學
國際經營管理碩士班(IMBA)
91932111
94
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0919321111
資料類型 thesis
dc.contributor.advisor 郭維裕zh_TW
dc.contributor.author (Authors) 彭貴田zh_TW
dc.creator (作者) 彭貴田zh_TW
dc.date (日期) 2005en_US
dc.date.accessioned 17-Sep-2009 18:55:11 (UTC+8)-
dc.date.available 17-Sep-2009 18:55:11 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 18:55:11 (UTC+8)-
dc.identifier (Other Identifiers) G0919321111en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/33960-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 國際經營管理碩士班(IMBA)zh_TW
dc.description (描述) 91932111zh_TW
dc.description (描述) 94zh_TW
dc.description.abstract (摘要) 傳統效率市場假設股價的波動是隨機的,亦即股價是無法預測。 近來的文獻指出股價的波動是不完全是隨機的,且股價的波動具有緩長記憶(long memory)的特性。在本文中我們以R/S分析發現臺灣股市的Hurst指數為0.68,即具有趨勢持續性(trend persistent)之效果,根據此依特性,我們根據Necula(2002)的研究,來評價台股選擇權,發現此新評價模式產生之價格較接近市場價格。zh_TW
dc.description.tableofcontents 第一章 序論………………………………………5

第一節 研究動機………………………………………………5
第二節 研究目的………………………………………………8
第三節 研究架構………………………………………………9

第二章 文獻探討…………………………………10

第一節 標準布朗運動與碎形布朗運動………………………10
第二節 非常態分佈與緩長記憶…...……………………….…11
第三節 選擇權評價簡介...………………………………….…13

第三章 研究方法…………………………………16

第一節 Hurst 指數與緩長記憶之關係………………………16
第二節 R/S分析………………………………………………18
第三節 修正之R/S分析……………………………………...19
第四節 DFA分析……………………………………………..20
第五節 緩長記憶之選擇權評價分析………………………...21

第四章 實證分析………………………………....23

第一節 TAII之Hurst 指數…………………………..………23
第二節 TAII之fBS選擇權評價與分析……………..………25

第五章 結論與後續建議………………………....29

第一節 結論……………………………………………………29
第二節 後續建議………………………………………………30

參考文獻……………………………………………………………..…31
zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0919321111en_US
dc.subject (關鍵詞) 緩長記憶zh_TW
dc.subject (關鍵詞) 碎形布朗運動zh_TW
dc.subject (關鍵詞) Hurst 指數zh_TW
dc.subject (關鍵詞) R/S分析zh_TW
dc.subject (關鍵詞) 碎形Black-Scholes選擇權評價zh_TW
dc.title (題名) 緩長記憶效應下的選擇權評價zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Bachelier, La Th´oerie de la Sp´eculation [Ph.D. thesis in mathematics], (1900), Ann. Sci. Ecole Norm. Super., S´er. 3, 17, 21.zh_TW
dc.relation.reference (參考文獻) 2. Backus, D.K. and S.E. Zin, (1993), “long-memory inflation uncertainty: Evidence from the term structure of interest rates.” Journal of Money, Credit and Banking 25, 681-700.zh_TW
dc.relation.reference (參考文獻) 3. Baillie, R.T., (1996), “Long-memory processes and fractional integration in econometrics.” Journal of Econometrics 73, 5-5zh_TW
dc.relation.reference (參考文獻) 4. Baillie, R.T., C.-F. Chung, and M.A. Tieslau,( 1995), Analyzing inflation by the fractional integrated ARFIMA-GARCH model. Journal of Applied Econometrics 11, 23-40.zh_TW
dc.relation.reference (參考文獻) 5. Beran, J., (1994), “Statistics for Long-Memory Processes.” Chapman & Hall.zh_TW
dc.relation.reference (參考文獻) 6. Black, F., and M. Scholes, (1972) ”The Valuation of Option Contracts and a Test of Market Efficiency,” Journal of Finance, 27 - 2, May, 399 - 418.zh_TW
dc.relation.reference (參考文獻) 7. Black, F., and M. Scholes, (1973) “The pricing of options and corporate liabilities”, Journal of Political Economy , vol.81:3,637-54.zh_TW
dc.relation.reference (參考文獻) 8. Costa R. L. and Vasconcelos G. L. (2003), Physica A 329, 231.zh_TW
dc.relation.reference (參考文獻) 9. Di Matteo T., Aste T., M. Dacorogna M., Physica A 324, 183 (2003); Cond-Mat preprint 0302434, 2003.zh_TW
dc.relation.reference (參考文獻) 10. Diebold, F.X. and G.D. Rudebusch, (1989), “Long-memory and persistence in aggregate output.” Journal of Monetary Economics 24, 189-209.zh_TW
dc.relation.reference (參考文獻) 11. Embrechts, Paul and Makoto Maejima. (2002), “Selfsimilar Processes.” Princeton University Press.zh_TW
dc.relation.reference (參考文獻) 12. Fama E. F. (1965), “Tha Behavior of Stock-Market Prices,” The Journal of Business of the University of Chicago, 38, no.1zh_TW
dc.relation.reference (參考文獻) 13. Fama E. F. (1970), “Efficient capital market: A review”, J. Finance 383-417zh_TW
dc.relation.reference (參考文獻) 14. Fleming, J., (1998), "The quality of market volatility forecasts implied by S&P100 index options prices", Journal of Empirical Finance, vol.5, 317-345.zh_TW
dc.relation.reference (參考文獻) 15. Grant, D., G. Vora, and D. Weeks, (1996), "Simulation and the Early-Exercise Option Problem," Journal of Financial Engineering, vol.5(3), 211-227.zh_TW
dc.relation.reference (參考文獻) 16. Grau-Carles P. (2000), Physica A , 287-396.zh_TW
dc.relation.reference (參考文獻) 17. Harrison, M. and D. Kreps, (1979), “Martingales and Multiperiod Securities Markets”, Journal of Economic Theory, vol.20, 381-408zh_TW
dc.relation.reference (參考文獻) 18. Hassler, U. and J. Wolters, (1995), “Long-memory in inflation rates: International evidence.” Journal of Business and Economic Statistics, vol.13, 37-45.zh_TW
dc.relation.reference (參考文獻) 19. Hu, Y. and Øksendal, B (2000), “Fractional white noise calculus and applications to finance”, Preprint, University of Oslo.zh_TW
dc.relation.reference (參考文獻) 20. Hurst, H. (1951), “Long term storage capacity of reservoirs”, Transactions of the American Society of Civil Engineers. Vol.116, 770-790.zh_TW
dc.relation.reference (參考文獻) 21. Jorion, P., (1995), “Predicting volatility in the foreign exchange market”, Journal of Finance. vol.50, 507-528zh_TW
dc.relation.reference (參考文獻) 22. Lo, A.W., (1991), “Long-term memory in stock market prices.” Econometrica, vol.59, 1279-1313.zh_TW
dc.relation.reference (參考文獻) 23. Mandelbrot B. B., (1963), J. Business(Chicago), vol.36, 394zh_TW
dc.relation.reference (參考文獻) 24. Mandelbrot, B. B. and Hudson, R. L. (2004). “The Behavior of Markets: A Fractal View of Risk, Ruin and Reward.” Basic Books, New York, NY.zh_TW
dc.relation.reference (參考文獻) 25. Mandelbrot, B.B., and H.W. Taylor, (1967), “On the distributions of stock price differences". Operations Research., vol.15, 1057-1062.zh_TW
dc.relation.reference (參考文獻) 26. Mandelbrot B.B. and J. W. Van Ness, (1968), SIAM Review 10, 422-437.zh_TW
dc.relation.reference (參考文獻) 27. Mandelbrot, B.B., (1971),”A Fast Fractional Gaussian Noise Generator”, Water Resources Research, 7, 543-553.zh_TW
dc.relation.reference (參考文獻) 28. Mandelbrot B. B., (1997) “Fractals and scaling in finance” Springer, New York,zh_TW
dc.relation.reference (參考文獻) 29. Mantegna R. and H. E. Stanley, (2000), “An Introduction to Econophysics”,Cambridge Univ. Press, Cambridge.zh_TW
dc.relation.reference (參考文獻) 30. Matacz A., (2000), Int. J. Theor. Appl. Financ. 3, 143-160.zh_TW
dc.relation.reference (參考文獻) 31. Miranda L. C. and R. Riera, (2001), Physica A 297, 509-520.zh_TW
dc.relation.reference (參考文獻) 32. Necula, Ciprian (2002), “Option Pricing in a Fractional Brownian Motion Environment”, Draft, Academy of Economic Studies, Bucharest, Romania.zh_TW
dc.relation.reference (參考文獻) 33. Osborne, M.F.M. (1959), “Brownian Motion in The Stock market.”Operations Research. vol. 7, 145-173.zh_TW
dc.relation.reference (參考文獻) 34. Peng, C.-K., S.V. Buldyrev, S. Havlin, M. Simons, and H.E. Stanley, 1994, Goldberger AL., “Mosaic organization of DNA nucleotides”, Physical Review E49, 1685-1689.zh_TW
dc.relation.reference (參考文獻) 35. Peters E. E.,(1991), “Chaos and order in capital markets”, Wiley, New York.zh_TW
dc.relation.reference (參考文獻) 36. Peters E. E.,(1994), “Fractal Market Analysis: Applying Chaos Theory to Investment and Economics”, Wiley, New York.zh_TW
dc.relation.reference (參考文獻) 37. Razdan, A. (2002)., “Scaling in the Bombay stock exchange index.” ramana-Journal of physics, Vol. 58, No. 3, March 2002, p. 537-544zh_TW
dc.relation.reference (參考文獻) 38. Rydberg, T. (1997), “Why Financial Data are Interesting to Statisticians”, Centre for Analytical Finance, Aarhus UniversityWorking Paper 5.zh_TW
dc.relation.reference (參考文獻) 39. Samuelson, P.A. (1964). “Rational Theory of Warrant Pricing. In The Random character of Stock Market Prices”, Ed. P. Cootner, pp 506-532, Cambridge, MIT Press.zh_TW
dc.relation.reference (參考文獻) 40. Schoutens W., (2003), “L´evy Processes in Finance: Pricing Financial Derivatives”, Wiley.zh_TW
dc.relation.reference (參考文獻) 41. Shea, G.S., (1991), “Uncertainty and implied variance bounds in long-memory models of the interest rate term structure.” Empirical Economics, vol. 16, 287-312.zh_TW
dc.relation.reference (參考文獻) 42. Shiryaev A. N., (1999), “Essentials of Stochastic Finance: Facts, Models,Theory, World Scientific”, Singapore.zh_TW
dc.relation.reference (參考文獻) 43. Teverovsky, V., M.S. Taqqu, and W. Willinger, (1999), “A critical look to Lo’s modified R/S statistics.” Journal of Statistical Planning and Inference, vol. 80, 211-227.zh_TW
dc.relation.reference (參考文獻) 44. Vandewalle N., Ausloos M., (1997), Physica A 246-454.zh_TW
dc.relation.reference (參考文獻) 45. Wiener N., J. (1923), Math. Phys. Math. 2, 131.zh_TW