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題名 以FIGARCH模型估計長期利率期貨風險值
Modeling Daily Value-at-Risk for Long-term Interest Rate Futures Using FIGARCH Models
作者 吳秉宗
Wu,Pinh-Tsung
貢獻者 謝淑貞
Shieh,Shwu-Jane
吳秉宗
Wu,Pinh-Tsung
關鍵詞 長期記憶性
部分整合自回歸條件變異數
風險值
利率期貨
Long Memory
FIGARCH
Value-at-Risk
Interest rate futures
日期 2004
上傳時間 11-Sep-2009 17:04:40 (UTC+8)
摘要 近幾年,風險值已經成為金融機構風險控管的重要工具。它的明確及簡單易懂是其讓人接受的原因,加上巴塞爾銀行監理委員會在1996提出的巴塞爾協定修正,規定銀行將市場風險因素納入考量,並允許銀行自行發展內部模型,以風險值模型衡量市場風險後,各種風險值的估算方法相繼被提出。
      本篇論文是使用部分整合自回歸條件變異數(Fractional Integrated Generalized Autoregressive Conditional Heteroskedasticity,簡稱FIGARCH)計算長期利率期貨多空部位的每日風險值。選取的三支長期利率期貨是在芝加哥期貨交易所掛牌的三十年期美國政府債券期貨(TB)、十年期美國政府債券期貨(TN)
     與十年期市政債券指數期貨(MNI)。
      利率期貨的研究在過去文獻中,甚少被提及。但隨著利率型商品日新月異的發展,以利率期貨避險的需求也與日遽增。尤其在台灣,利率期貨更是今年新登場的期貨商品。因此,我選擇利率期貨作為研究標的,藉由以FIGARCH模型來配適波動性,提供避險者一個估算風險值的方法。
      FIGARCH模型係由Baillie、Bollerslev與Mikkelsen於1996所提出,與傳統GARCH模型所不同的是,FIGARCH模型特別適用於描述具有波動性長期記憶(Long Memory)性質的資料。所謂長期記憶性,是指衝擊所造成的持續性是以緩慢的雙曲線速率衰退。而許多市場實證分析均指出,FIGARCH較適合用來描述金融市場上的波動性。此外,本研究的風險值計算,除了一般實務界常用的常態分配以外,還考慮了t分配與偏斜t分配,以捕捉財務資料常見的厚尾與偏斜的特性。
      而實證結果顯示,長期利率期貨報酬率的波動性確實存在長期記憶性,所以FIGARCH(1,d,1)模型可以適切地估算長期利率期貨的每日風險值,不論在樣本內或樣本外的風險值計算均優於傳統GARCH(1,1)模型的計算結果。至於各種不同分配的比較,在樣本內的風險值計算,當α=0.05時,常態分配FIGARCH(1,d,1)模型表現較佳;當α=0.025到0.0025時,t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳,而偏斜t分配FIGARCH又稍微優於t分配FIGARCH(1,d,1)模型。
      而樣本外的風險值預測,則有不同的結果,當α=0.05,t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳;而α=0.01時,常態分配FIGARCH(1,d,1)模型表現較佳。而且t分配與偏斜t分配FIGARCH(1,d,1)模型在α=0.01會出現太過保守的情形,出現失敗率(failure rate)為零,高估風險值。
Value-at-Risk (VaR) has become the standard measure used to quantify market risk recently, and it is defined as the maximum expected loss in the value of an asset or portfolio, for a given probability α at a determined time period. This article uses the FIGARCH(1,d,1) models to calculate daily VaR for long-term interest rate futures returns for long and short trading positions based on the normal, the Student-t, and the skewed Student-t error distributions. The U.S. Treasury bonds futures, Treasury notes futures, and municipal notes index futures of daily frequency are studied.
      The empirical results show that returns series for three interest rate futures all have long memory in volatility, and should be modeled using fractional integrated models. Besides, the in-sample and out-of-sample VaR values generated using FIGARCH(1,d,1) models are more accurate than those generated using traditional GARCH(1,1) models. For different distributions among FIGARCH(1,d,1) models, the normal FIGARCH(1,d,1) models are preferred for in-sample VaR computing whenα=0.05, and the Student-t and skewed Student-t models perform better for in-sample VaR computing whenα=0.025-0.0025. Nonetheless, for out-of-sample VaR, the Student-t and skewed Student-t FIGARCH(1,d,1) models perform better in the case α=0.05 while the normal FIGARCH(1,d,1) models perform better in the case α=0.01. The VaR values obtained by the Student-t and skewed Student-t FIGARCH(1,d,1) models are too conservative whenα=0.01.
參考文獻 1. Alexander, C.O. and C. Leigh, 1997, “On the covariance matrices used in VaR models,” Journal of Derivatives, spring 1997, pp.50-62
2. Baillie, R.T.,1996, “Long memory processes and fractional integration in econometrics,” Journal of Econometrics, 73, pp.5-59.
3. Baillie, R.T., T. Bollerslev, and H.O. Mikkelsen, 1996, “Fractionally integrated generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, 74, pp.3-30.
4. Baillie, R.T., A.A. Cecen, and Han, Y.W., 2000, “High frequency Deutsche Mark-US dollar returns: FIGARCH representations and nonlinearities,” Multinational Finance Journal, 4, pp.247-267.
5. Beder, T.S., 1995, “VaR: seductive but dangerous,” Financial Analysis Journal, Sep/Oct 1995, pp.12-24.
6. Beine, M., S. Laurent, and C. Lecourt, 2002, “Accounting for conditional leptokurtosis and closing days effect in FIGARCH models of daily exchange rates,” Applied Financial Economics, 12, pp.589-600.
7. Beltratti, A. and C. Morana, 1999, “Computing value at risk with high frequency data,” Journal of Empirical Finance, 6, pp.431-455.
8. Bollerslev, T., 1986, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, 31, pp.307-327.
9. Bollerslev, T., 1987, “A conditional heteroskedastic time series model for speculative prices and rates of return,” Review of Economics and Statistics, 69, pp.542-547.
10. Bollerslev, T. and H.O. Mikkelsen, 1996, “Modeling and pricing long- memory in stock market volatility,” Journal of Econometrics, 73, pp.151-184.
11. Bollerslev, T. and H.O. Mikkelsen, 1999, “Long-term equity anticipation securities and stock market volatility dynamics,” Journal of Econometrics, 92, pp.75-99.
12. Bollerslev, T. and D. Jubinski, 1999. "Equity trading volume and volatility: latent information arrivals and common long-run dependencies," Journal of Business and Economic Statistics, Vol. 17 (1), pp. 9-21.
13. Booth, G.G. and Y. Tse, 1995, “Long memory in interest rate futures markets: a fractional cointegration analysis,” Journal of Futures Markets, 15, No.5, pp.573-584.
14. Breidt, F.J., Crato, N. and P. de Lima, 1998, “The detection and estimation of long memory in stochastic volatility,” Journal of Econometrics, 83, pp.325-348.
15. Dickey, D.A., and W.A. Fuller, 1979, “Distribution of the estimators for autoregressive times series with a unit root,” Journal of the American Statistical Association, Vol.74, pp.427-431.
16. Diebold, F.X. and J.A. Lopez, 1996, “Forecast evaluation and combination,” Handbooks of Statistics, Vol. 14, pp.241-268.
17. Ding, Z., C.W.J. Granger, and R.F. Engle, 1993, “A long memory property of stock market returns and a new model,” Journal of Empirical Finance, 1, pp 83-106.
18. Ding, Z. and C.W.J. Granger, 1996, “Modeling volatility persistence of speculative returns: A new approach,” Journal of Econometrics, 73, pp.185-215.
19. Doornik, A., G. Draisma, and M. Ooms, 2001, Introduction to Ox, version 3, Timberlake Consultants Ltd.
20. Enders, W., 1995, Applied Econometrics Time Series, John Wiley & Sons, Inc.
21. Engle, R.F., 1982, “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation,” Econometrica, 50, pp. 987-1007.
22. Engle, R.F. and T. Bollerslev, 1986, “Modeling the persistence of conditional variance,” Econometric Reviews, 5, pp.1-50.
23. Engle, J. and M. Gizycki, 1999, “Conservatism, accuracy, and efficiency: comparing Value-at-Risk models,” Working paper, Australian Prudential Regulation Authority.
24. Fung, H.G, and A.W. Lo, 1993, “Memory in interest rate futures,” Journal of Futures Markets, 13, No.8, pp.865-872.
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26. Giot, P., 2003, “Market risk models for intraday data,” University of Namur working paper.
27. Giot, P. and S. Laurent, 2003, “Value-at-risk for long and short trading positions,” Journal of Applied Economics, 18, pp.641-664.
28. Giot, P. and S. Laurent, 2001, “Modelling value at risk using realized volatility and ARCH type models,” Mimeo. University of Maastricht.
29. Grau, T.M.N., 2002, “Modelling daily value-at-risk using FIGARCH type models,” University of Alicnte working paper.
30. Hendricks, D., 1996, “Evaluation of value-at-risk models using historical data,” Federal Reserve Bank of New York Economics Policy Review, April.
31. Hull, J. and A. White, 1998, “Value at risk when daily changes in market variables are not normally distributed,” The Journal of Derivatives, 5, pp.9-19.
32. Hull, J., 1995, Introduction to Futures and Options Markets, Prentice Hall.
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35. Jorion, P., 1996, “Rsik2: measuring the risk in value at risk,” Financial Analysts Journal, Nov/Dec 1996, 52, pp.47-56.
36. Jorion, P., 2000, Value at Risk: The New Benchmark for Managing Financial Risk, 2nd edition, McGraw-Hill.
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38. Kwiaowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin, 1992, “Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?” Journal of Econometrics, 54, pp.159-178.
39. Lambert, P., and S. Laurent, 2000, ”Modelling skewness dynamics in series of financial data. institute de statistique”, Louvain-la-Neuve.
40. Lambert, P. and S. Laurent, 2001, “Modeling financial time series using GARCH-type models and a skewed student density,” Mimeo, Universit´e de Li´ege.
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(http://www.core.ucl.ac.be:16080/~laurent/)
42. Lee, D. and P. Schmidt, 1996, “On the power of the KPSS test of stationarity against fractionally integrated alternatives,” Journal of Econometrics, 73, pp.285-302.
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描述 碩士
國立政治大學
國際經營與貿易研究所
91351014
93
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091351014
資料類型 thesis
dc.contributor.advisor 謝淑貞zh_TW
dc.contributor.advisor Shieh,Shwu-Janeen_US
dc.contributor.author (Authors) 吳秉宗zh_TW
dc.contributor.author (Authors) Wu,Pinh-Tsungen_US
dc.creator (作者) 吳秉宗zh_TW
dc.creator (作者) Wu,Pinh-Tsungen_US
dc.date (日期) 2004en_US
dc.date.accessioned 11-Sep-2009 17:04:40 (UTC+8)-
dc.date.available 11-Sep-2009 17:04:40 (UTC+8)-
dc.date.issued (上傳時間) 11-Sep-2009 17:04:40 (UTC+8)-
dc.identifier (Other Identifiers) G0091351014en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/30021-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 國際經營與貿易研究所zh_TW
dc.description (描述) 91351014zh_TW
dc.description (描述) 93zh_TW
dc.description.abstract (摘要) 近幾年,風險值已經成為金融機構風險控管的重要工具。它的明確及簡單易懂是其讓人接受的原因,加上巴塞爾銀行監理委員會在1996提出的巴塞爾協定修正,規定銀行將市場風險因素納入考量,並允許銀行自行發展內部模型,以風險值模型衡量市場風險後,各種風險值的估算方法相繼被提出。
      本篇論文是使用部分整合自回歸條件變異數(Fractional Integrated Generalized Autoregressive Conditional Heteroskedasticity,簡稱FIGARCH)計算長期利率期貨多空部位的每日風險值。選取的三支長期利率期貨是在芝加哥期貨交易所掛牌的三十年期美國政府債券期貨(TB)、十年期美國政府債券期貨(TN)
     與十年期市政債券指數期貨(MNI)。
      利率期貨的研究在過去文獻中,甚少被提及。但隨著利率型商品日新月異的發展,以利率期貨避險的需求也與日遽增。尤其在台灣,利率期貨更是今年新登場的期貨商品。因此,我選擇利率期貨作為研究標的,藉由以FIGARCH模型來配適波動性,提供避險者一個估算風險值的方法。
      FIGARCH模型係由Baillie、Bollerslev與Mikkelsen於1996所提出,與傳統GARCH模型所不同的是,FIGARCH模型特別適用於描述具有波動性長期記憶(Long Memory)性質的資料。所謂長期記憶性,是指衝擊所造成的持續性是以緩慢的雙曲線速率衰退。而許多市場實證分析均指出,FIGARCH較適合用來描述金融市場上的波動性。此外,本研究的風險值計算,除了一般實務界常用的常態分配以外,還考慮了t分配與偏斜t分配,以捕捉財務資料常見的厚尾與偏斜的特性。
      而實證結果顯示,長期利率期貨報酬率的波動性確實存在長期記憶性,所以FIGARCH(1,d,1)模型可以適切地估算長期利率期貨的每日風險值,不論在樣本內或樣本外的風險值計算均優於傳統GARCH(1,1)模型的計算結果。至於各種不同分配的比較,在樣本內的風險值計算,當α=0.05時,常態分配FIGARCH(1,d,1)模型表現較佳;當α=0.025到0.0025時,t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳,而偏斜t分配FIGARCH又稍微優於t分配FIGARCH(1,d,1)模型。
      而樣本外的風險值預測,則有不同的結果,當α=0.05,t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳;而α=0.01時,常態分配FIGARCH(1,d,1)模型表現較佳。而且t分配與偏斜t分配FIGARCH(1,d,1)模型在α=0.01會出現太過保守的情形,出現失敗率(failure rate)為零,高估風險值。
zh_TW
dc.description.abstract (摘要) Value-at-Risk (VaR) has become the standard measure used to quantify market risk recently, and it is defined as the maximum expected loss in the value of an asset or portfolio, for a given probability α at a determined time period. This article uses the FIGARCH(1,d,1) models to calculate daily VaR for long-term interest rate futures returns for long and short trading positions based on the normal, the Student-t, and the skewed Student-t error distributions. The U.S. Treasury bonds futures, Treasury notes futures, and municipal notes index futures of daily frequency are studied.
      The empirical results show that returns series for three interest rate futures all have long memory in volatility, and should be modeled using fractional integrated models. Besides, the in-sample and out-of-sample VaR values generated using FIGARCH(1,d,1) models are more accurate than those generated using traditional GARCH(1,1) models. For different distributions among FIGARCH(1,d,1) models, the normal FIGARCH(1,d,1) models are preferred for in-sample VaR computing whenα=0.05, and the Student-t and skewed Student-t models perform better for in-sample VaR computing whenα=0.025-0.0025. Nonetheless, for out-of-sample VaR, the Student-t and skewed Student-t FIGARCH(1,d,1) models perform better in the case α=0.05 while the normal FIGARCH(1,d,1) models perform better in the case α=0.01. The VaR values obtained by the Student-t and skewed Student-t FIGARCH(1,d,1) models are too conservative whenα=0.01.
en_US
dc.description.tableofcontents Abstract 1
     1.Introduction 2
     2.Literature Review 5
      2.1 Long Memory and Fractional Integrated GARCH 5
      2.2 Value-at-Risk 9
      2.2.1 VaR Definition and Methods 9
      2.2.2 VaR Methods Comparison 12
     3.Data Description 16
     4.Methodology 22
      4.1 Unit Root Tests and Stationarity Test 22
      4.1.1 The ADF and PP Tests 22
      4.1.2 The KPSS Test 24
      4.2 Lo’s R/S Test 25
      4.3 Fractional Integrated GARCH Models 26
      4.4 Value-at-Risk Methodology 28
      4.5 Measure of Accuracy for VaR Estimates 33
      4.6 Volatility Forecasting Evaluation 34
     5.Empirical Results 36
      5.1 Unit Root Tests and Stationarity Test 36
      5.2 Long Memory in Volatility 36
      5.3 Estimating The Models 42
      5.4 In-Sample VaR Analysis 43
      5.5 Volatility Forecasting Performance 45
      5.6 Out-of-Sample VaR Analysis 45
     6.Concluding Remarks 69
     Appendix 71
     Reference 73
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091351014en_US
dc.subject (關鍵詞) 長期記憶性zh_TW
dc.subject (關鍵詞) 部分整合自回歸條件變異數zh_TW
dc.subject (關鍵詞) 風險值zh_TW
dc.subject (關鍵詞) 利率期貨zh_TW
dc.subject (關鍵詞) Long Memoryen_US
dc.subject (關鍵詞) FIGARCHen_US
dc.subject (關鍵詞) Value-at-Risken_US
dc.subject (關鍵詞) Interest rate futuresen_US
dc.title (題名) 以FIGARCH模型估計長期利率期貨風險值zh_TW
dc.title (題名) Modeling Daily Value-at-Risk for Long-term Interest Rate Futures Using FIGARCH Modelsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Alexander, C.O. and C. Leigh, 1997, “On the covariance matrices used in VaR models,” Journal of Derivatives, spring 1997, pp.50-62zh_TW
dc.relation.reference (參考文獻) 2. Baillie, R.T.,1996, “Long memory processes and fractional integration in econometrics,” Journal of Econometrics, 73, pp.5-59.zh_TW
dc.relation.reference (參考文獻) 3. Baillie, R.T., T. Bollerslev, and H.O. Mikkelsen, 1996, “Fractionally integrated generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, 74, pp.3-30.zh_TW
dc.relation.reference (參考文獻) 4. Baillie, R.T., A.A. Cecen, and Han, Y.W., 2000, “High frequency Deutsche Mark-US dollar returns: FIGARCH representations and nonlinearities,” Multinational Finance Journal, 4, pp.247-267.zh_TW
dc.relation.reference (參考文獻) 5. Beder, T.S., 1995, “VaR: seductive but dangerous,” Financial Analysis Journal, Sep/Oct 1995, pp.12-24.zh_TW
dc.relation.reference (參考文獻) 6. Beine, M., S. Laurent, and C. Lecourt, 2002, “Accounting for conditional leptokurtosis and closing days effect in FIGARCH models of daily exchange rates,” Applied Financial Economics, 12, pp.589-600.zh_TW
dc.relation.reference (參考文獻) 7. Beltratti, A. and C. Morana, 1999, “Computing value at risk with high frequency data,” Journal of Empirical Finance, 6, pp.431-455.zh_TW
dc.relation.reference (參考文獻) 8. Bollerslev, T., 1986, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, 31, pp.307-327.zh_TW
dc.relation.reference (參考文獻) 9. Bollerslev, T., 1987, “A conditional heteroskedastic time series model for speculative prices and rates of return,” Review of Economics and Statistics, 69, pp.542-547.zh_TW
dc.relation.reference (參考文獻) 10. Bollerslev, T. and H.O. Mikkelsen, 1996, “Modeling and pricing long- memory in stock market volatility,” Journal of Econometrics, 73, pp.151-184.zh_TW
dc.relation.reference (參考文獻) 11. Bollerslev, T. and H.O. Mikkelsen, 1999, “Long-term equity anticipation securities and stock market volatility dynamics,” Journal of Econometrics, 92, pp.75-99.zh_TW
dc.relation.reference (參考文獻) 12. Bollerslev, T. and D. Jubinski, 1999. "Equity trading volume and volatility: latent information arrivals and common long-run dependencies," Journal of Business and Economic Statistics, Vol. 17 (1), pp. 9-21.zh_TW
dc.relation.reference (參考文獻) 13. Booth, G.G. and Y. Tse, 1995, “Long memory in interest rate futures markets: a fractional cointegration analysis,” Journal of Futures Markets, 15, No.5, pp.573-584.zh_TW
dc.relation.reference (參考文獻) 14. Breidt, F.J., Crato, N. and P. de Lima, 1998, “The detection and estimation of long memory in stochastic volatility,” Journal of Econometrics, 83, pp.325-348.zh_TW
dc.relation.reference (參考文獻) 15. Dickey, D.A., and W.A. Fuller, 1979, “Distribution of the estimators for autoregressive times series with a unit root,” Journal of the American Statistical Association, Vol.74, pp.427-431.zh_TW
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