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題名 運用長期記憶模型於估計股票指數期貨之風險值
Estimating Value-at-Risk for stock index futures using Double Long-memory Models
作者 唐大倫
Tang,Ta-lun Tang
貢獻者 謝淑貞
唐大倫
Tang,Ta-lun Tang
關鍵詞 長期記憶性
不對稱
風險值
ARFIMA
FIGARCH
Long memory
Asymmetry
Value-at-Risk
日期 2003
上傳時間 11-Sep-2009 17:05:05 (UTC+8)
摘要 在本篇文章中,我們採用長期記憶模型來估計S&P500、Nasdaq100和Dow Jones Industrial Index三個股票指數期貨的日收盤價的風險值。為了更準確地計算風險值,本文採用常態分配、t分配以及偏斜t分配來做模型估計以及風險值之計算。有鑒於大多數探討風險值的文獻只考慮買入部位的風險,本研究除了估計買入部位的風險值,也估計放空部位的風險值,以期更能全面性地估算風險。實證結果顯示,ARFIMA-FIGARCH模型配合偏斜t分配較其他兩種分配更能精確地估算樣本內的風險值。基於ARFIMA-FIGARCH模型配合偏斜t分配在樣本內風險值計算的優異表現,我們利用此模型搭配來實際求算樣本外風險值。結果如同樣本內風險值一般,ARFIMA-FIGARCH模型配合偏斜t分配在樣本外也有相當好的風險預測能力。
In this thesis, we estimate Value-at-Risk (VaR) for daily closing price of three stock index futures contracts, S&P500, Nasdaq100, and Dow Jones, using the double long memory models. Due to the existence of a long-term persistence characterized in our data, the ARFIMA-FIGARCH models are used to compute the VaR. In order to investigate better, three kinds of density distributions, normal, Student-t, and skewed Student-t distributions, are used for estimating models and computing the VaR. In addition to the VaR for the long trading positions which most researches focus on to date, the VaR for the short trading positions are calculated as well in this study. From the empirical results we show that for the three stock index futures, the ARFIMA-FIGARCH models with skewed Student-t distribution perform better in computing in-sample VaR both in long and short trading positions than symmetric models and has a quite excellent performance in forecasting out-of-sample VaR as well.
參考文獻 Alexander, C. O. and Leigh, C. T., 1997, On the covariance metrices used in value-at-risk model, The Journal of Derivatives, 50-62.
Baillie, R. T., Bollerslev, T., and Mikkelsen, H., 1996, Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 74, 3-30.
Baillie, R. T., Chung, C. -F., and Tieslau, M. A., 1996, Analyzing inflation by the fractionally integrated ARFIMA-GARCH model, Journal of Applied Econometrics 11, 23-40.
Barkoulas, J. T. and Baum, C. F., Long term dependence in stock returns, Working Paper, Department of Economics, Boston College, USA.
Beine, M. and Laurent, S., 2003, Central bank interventions and jumps in double long memory models of daily exchange rate, Working Paper.
Bollerslev, T., 1986, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31, 307-327.
Bollerslev, T. and Mikkelen, H. O., 1996, Modeling and pricing long memory in stock market volatility, Journal of Econometrics 73, 151-184.
Brunetti, C. and Gilbert, C. L., 2000, Bivariate FIGARCH and fractional cointegration, Journal of Empirical Finance 7, 509-530.
Chou, C. H., 2000, The performance of VaR measurements- the empirical studies of currency exchange rates, Graduate Institute of Financa, Fu Jen Catholic University.
Christoffersen, P. F. and Diebold, F. X., 2000, How relevant is volatility forecasting for financial risk management? Review of Economics and Statistics 82, 1-11.
Ding, Z., Granger, C. W. J., and Engle, R. F., 1993, A long memory property of stock market returns and a new model, Journal of Empirical Finance 1, 83-106.
Dueker, M. and Asea, P. K., 1995, Non-monotonic long memory dynamics in black-market exchange rates, Working Paper, Federal Reserve Bank of ST. Louis.
Engle, R. F., 1982, Autoregressive conditional heteroskedasticity with estimates of the variance of united kingdom inflation, Econometrica 50, 987-1007.
Giot, P. and Laurent, S., 2003, Value-at-risk for long and short trading positions, Journal of Applied Econometrics 18, 641-664.
Goorbergh, R. V. D. and Vlaar, P., 1999, Value-at-risk analysis of stock returns historical simulation, variance techniques or tail index estimation, http://www.gloriamundi.org.
Granger, C. W. J. and Ding, Z. 1996, Varieties of long memory models, Journal of Econometrics 73, 61-77.
Henry, O. T., 2000, Long memory in stock returns: some international evidence, Working Paper, Department of Economics, The University of Melbourne, Australia.
Jorion, P., 2000, Value-at-risk: The New Benchmark for Managina Financial Risk, McGraw-Hill.
Kupiec, P., 1995, Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives 2, 174-184.
Lambert, P. and Laurent, S., 2000, Modeling skewness dynamics in series of financial data, Discussion Paper, Institute de Statistique, Louvain-la-Neuve.
Lo, A. W., 1991, Long-term memory in stock market price, Econometrica 59, 1279-1313.
Liu, S. and Brorsen, B., 1995, Maximun likelihood estimation of a GARCH-stable model, Journal of Applied Econometrics 2, 273-185.
Shieh, S. –J., 2004, Modeling daily value-at-risk using FIAPARCH model with (skewed) Student-t density, Working Paper, Department of International Trade, National Cheng-chi University, Taiwan.
Shieh, S. –J., 2003, Mean reversion in stock index futures markets, Working Paper, Department of International Trade, National Cheng-chi University, Taiwan.
Sriananthakumar, S. and Silvapulle, S., 2003, Estimating value at risks for short and long trading positions, Working Paper, Department of Economics and Business Statistics, Monash University, Australia.
Tse, Y. K., Anh, V. V., and Tieng, Q., Maximun likelihood estimation of the fractional differencing parameter in an ARFIMA model using wavelets, Working Paper.
Wung, S. B., 1999, The market risk measurement of the warrants of the issuer, The Department of Economics, Soochow University, Taiwan.
描述 碩士
國立政治大學
國際經營與貿易研究所
91351022
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091351022
資料類型 thesis
dc.contributor.advisor 謝淑貞zh_TW
dc.contributor.author (Authors) 唐大倫zh_TW
dc.contributor.author (Authors) Tang,Ta-lun Tangen_US
dc.creator (作者) 唐大倫zh_TW
dc.creator (作者) Tang,Ta-lun Tangen_US
dc.date (日期) 2003en_US
dc.date.accessioned 11-Sep-2009 17:05:05 (UTC+8)-
dc.date.available 11-Sep-2009 17:05:05 (UTC+8)-
dc.date.issued (上傳時間) 11-Sep-2009 17:05:05 (UTC+8)-
dc.identifier (Other Identifiers) G0091351022en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/30024-
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) 91351022zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 在本篇文章中,我們採用長期記憶模型來估計S&P500、Nasdaq100和Dow Jones Industrial Index三個股票指數期貨的日收盤價的風險值。為了更準確地計算風險值,本文採用常態分配、t分配以及偏斜t分配來做模型估計以及風險值之計算。有鑒於大多數探討風險值的文獻只考慮買入部位的風險,本研究除了估計買入部位的風險值,也估計放空部位的風險值,以期更能全面性地估算風險。實證結果顯示,ARFIMA-FIGARCH模型配合偏斜t分配較其他兩種分配更能精確地估算樣本內的風險值。基於ARFIMA-FIGARCH模型配合偏斜t分配在樣本內風險值計算的優異表現,我們利用此模型搭配來實際求算樣本外風險值。結果如同樣本內風險值一般,ARFIMA-FIGARCH模型配合偏斜t分配在樣本外也有相當好的風險預測能力。zh_TW
dc.description.abstract (摘要) In this thesis, we estimate Value-at-Risk (VaR) for daily closing price of three stock index futures contracts, S&P500, Nasdaq100, and Dow Jones, using the double long memory models. Due to the existence of a long-term persistence characterized in our data, the ARFIMA-FIGARCH models are used to compute the VaR. In order to investigate better, three kinds of density distributions, normal, Student-t, and skewed Student-t distributions, are used for estimating models and computing the VaR. In addition to the VaR for the long trading positions which most researches focus on to date, the VaR for the short trading positions are calculated as well in this study. From the empirical results we show that for the three stock index futures, the ARFIMA-FIGARCH models with skewed Student-t distribution perform better in computing in-sample VaR both in long and short trading positions than symmetric models and has a quite excellent performance in forecasting out-of-sample VaR as well.en_US
dc.description.tableofcontents Contents
     
     1.Introduction ......................................... 6
     
     2.Literature Review .....................................8
     
     3.Methodology ..........................................14
      3.1 Unit Root Tests ..................................14
      3.1.1 The Augmented Dickey-Fuller Test............ 15
      3.1.2 The Phillips-Perron Test.................... 16
     
      3.2 Detecting Long Memory in the Time Series......... 16
     
      3.3 ARFIMA-FIGARCH Model............................. 18
     
      3.4 Distribution .................................... 20
     
      3.5 VaR model and LR Test ............................22
      3.5.1 VaR Model .................................. 22
      3.5.2 Kupiec LR Test ........................... 23
     
     4. Data and Empirical Results...........................24
      4.1 Data............................................. 25
     
      4.2 Estimation Results: ARFIMA-FIGARCH Model......... 33
     
      4.3 VaR Computation ................................. 37
      4.3.1 In-sample VaR Computation .................. 38
      4.3.2 Out-of-sample VaR Computation .............. 40
     
     5. Conclusions .........................................45
     
     Reference...............................................48
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091351022en_US
dc.subject (關鍵詞) 長期記憶性zh_TW
dc.subject (關鍵詞) 不對稱zh_TW
dc.subject (關鍵詞) 風險值zh_TW
dc.subject (關鍵詞) ARFIMAen_US
dc.subject (關鍵詞) FIGARCHen_US
dc.subject (關鍵詞) Long memoryen_US
dc.subject (關鍵詞) Asymmetryen_US
dc.subject (關鍵詞) Value-at-Risken_US
dc.title (題名) 運用長期記憶模型於估計股票指數期貨之風險值zh_TW
dc.title (題名) Estimating Value-at-Risk for stock index futures using Double Long-memory Modelsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Alexander, C. O. and Leigh, C. T., 1997, On the covariance metrices used in value-at-risk model, The Journal of Derivatives, 50-62.zh_TW
dc.relation.reference (參考文獻) Baillie, R. T., Bollerslev, T., and Mikkelsen, H., 1996, Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 74, 3-30.zh_TW
dc.relation.reference (參考文獻) Baillie, R. T., Chung, C. -F., and Tieslau, M. A., 1996, Analyzing inflation by the fractionally integrated ARFIMA-GARCH model, Journal of Applied Econometrics 11, 23-40.zh_TW
dc.relation.reference (參考文獻) Barkoulas, J. T. and Baum, C. F., Long term dependence in stock returns, Working Paper, Department of Economics, Boston College, USA.zh_TW
dc.relation.reference (參考文獻) Beine, M. and Laurent, S., 2003, Central bank interventions and jumps in double long memory models of daily exchange rate, Working Paper.zh_TW
dc.relation.reference (參考文獻) Bollerslev, T., 1986, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31, 307-327.zh_TW
dc.relation.reference (參考文獻) Bollerslev, T. and Mikkelen, H. O., 1996, Modeling and pricing long memory in stock market volatility, Journal of Econometrics 73, 151-184.zh_TW
dc.relation.reference (參考文獻) Brunetti, C. and Gilbert, C. L., 2000, Bivariate FIGARCH and fractional cointegration, Journal of Empirical Finance 7, 509-530.zh_TW
dc.relation.reference (參考文獻) Chou, C. H., 2000, The performance of VaR measurements- the empirical studies of currency exchange rates, Graduate Institute of Financa, Fu Jen Catholic University.zh_TW
dc.relation.reference (參考文獻) Christoffersen, P. F. and Diebold, F. X., 2000, How relevant is volatility forecasting for financial risk management? Review of Economics and Statistics 82, 1-11.zh_TW
dc.relation.reference (參考文獻) Ding, Z., Granger, C. W. J., and Engle, R. F., 1993, A long memory property of stock market returns and a new model, Journal of Empirical Finance 1, 83-106.zh_TW
dc.relation.reference (參考文獻) Dueker, M. and Asea, P. K., 1995, Non-monotonic long memory dynamics in black-market exchange rates, Working Paper, Federal Reserve Bank of ST. Louis.zh_TW
dc.relation.reference (參考文獻) Engle, R. F., 1982, Autoregressive conditional heteroskedasticity with estimates of the variance of united kingdom inflation, Econometrica 50, 987-1007.zh_TW
dc.relation.reference (參考文獻) Giot, P. and Laurent, S., 2003, Value-at-risk for long and short trading positions, Journal of Applied Econometrics 18, 641-664.zh_TW
dc.relation.reference (參考文獻) Goorbergh, R. V. D. and Vlaar, P., 1999, Value-at-risk analysis of stock returns historical simulation, variance techniques or tail index estimation, http://www.gloriamundi.org.zh_TW
dc.relation.reference (參考文獻) Granger, C. W. J. and Ding, Z. 1996, Varieties of long memory models, Journal of Econometrics 73, 61-77.zh_TW
dc.relation.reference (參考文獻) Henry, O. T., 2000, Long memory in stock returns: some international evidence, Working Paper, Department of Economics, The University of Melbourne, Australia.zh_TW
dc.relation.reference (參考文獻) Jorion, P., 2000, Value-at-risk: The New Benchmark for Managina Financial Risk, McGraw-Hill.zh_TW
dc.relation.reference (參考文獻) Kupiec, P., 1995, Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives 2, 174-184.zh_TW
dc.relation.reference (參考文獻) Lambert, P. and Laurent, S., 2000, Modeling skewness dynamics in series of financial data, Discussion Paper, Institute de Statistique, Louvain-la-Neuve.zh_TW
dc.relation.reference (參考文獻) Lo, A. W., 1991, Long-term memory in stock market price, Econometrica 59, 1279-1313.zh_TW
dc.relation.reference (參考文獻) Liu, S. and Brorsen, B., 1995, Maximun likelihood estimation of a GARCH-stable model, Journal of Applied Econometrics 2, 273-185.zh_TW
dc.relation.reference (參考文獻) Shieh, S. –J., 2004, Modeling daily value-at-risk using FIAPARCH model with (skewed) Student-t density, Working Paper, Department of International Trade, National Cheng-chi University, Taiwan.zh_TW
dc.relation.reference (參考文獻) Shieh, S. –J., 2003, Mean reversion in stock index futures markets, Working Paper, Department of International Trade, National Cheng-chi University, Taiwan.zh_TW
dc.relation.reference (參考文獻) Sriananthakumar, S. and Silvapulle, S., 2003, Estimating value at risks for short and long trading positions, Working Paper, Department of Economics and Business Statistics, Monash University, Australia.zh_TW
dc.relation.reference (參考文獻) Tse, Y. K., Anh, V. V., and Tieng, Q., Maximun likelihood estimation of the fractional differencing parameter in an ARFIMA model using wavelets, Working Paper.zh_TW
dc.relation.reference (參考文獻) Wung, S. B., 1999, The market risk measurement of the warrants of the issuer, The Department of Economics, Soochow University, Taiwan.zh_TW