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題名 仿射AFNS利率模型參數之校準方法探討
Calibrating the arbitrage-free Nelson-Siegel model作者 陳文忠
Chen, Wen-Chung貢獻者 謝明華
Hsieh, Ming-Hua
陳文忠
Chen, Wen-Chung關鍵詞 利率期限模型
參數校準
AFNS 模型
Nelder-Mead 方法
Term Structure Model
Calibration
AFNS model
Nelder-Mead日期 2020 上傳時間 2-Sep-2020 11:51:18 (UTC+8) 摘要 Arbitrage Free Nelson Siegel model (AFNS model) 為滿足無套利條件且具優良配適與預測能力之利率模型，本研究探討 AFNS model 參數之校準方法。文中以台灣公債利率資料與美國公債利率資料為例，使用兩種不同的方式，搭配最小平方法與 Nelder-Mead 方法來校準參數，並比較其計算結果之差異。本文發現第二種參數校準方式可以有效率且準確地找出參數校準值。
Arbitrage-Free Nelson Siegel models is an affine term structure model that satisfies no-arbitrage condition and displays good fit and superior forecasting performance. This study explores the calibration method of AFNS model parameters. In this paper, the interest rate data of Taiwan government bonds and US government bonds are used as examples. Two methods are used, combined with the least square method and the Nelder-Mead method to calibrate the parameters, and the differences in the calculation results are compared. This article found that the second calibration method can efficiently and accurately find the parameter calibration value.參考文獻 Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.Christensen, J. H., Diebold, F. X., & Rudebusch, G. D. (2011). The affine arbitragefree class of Nelson–Siegel term structure models. Journal of Econometrics, 164(1), 4-20.Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (2005). A theory of the term structure of interest rates. In Theory of Valuation (pp. 129-164). World Scientific.Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. Journal of econometrics, 130(2), 337-364.Duffee, G. R. (2002). Term premia and interest rate forecasts in affine models. The Journal of Finance, 57(1), 405-443.Duffie, D., & Kan, R. (1996). A yield‐factor model of interest rates. Mathematical finance, 6(4), 379-406.Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica: Journal of the Econometric Society, 77-105.Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The review of financial studies, 3(4), 573-592.IAIS, ICS, Retrieved June 1 2020, from: https://www.iaisweb.org/page/supervisorymaterial/insurance-capital-standardMarek, J. (2015). The Nelson-Siegel Model: Present Application and Alternative Lambda Determination.Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The computer journal, 7(4), 308-313.Nelson, C. R., & Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of business, 473-489.Singleton, K. J. (2009). Empirical dynamic asset pricing: model specification and econometric assessment. Princeton University Press.Tourrucôo, F., Caldeira, J. F., Moura, G., & Santos, A. (2016). Forecasting the yield curve with the arbitrage-free dynamic Nelson–Siegel model: Brazilian evidence. Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting]. Niterói: ANPEC-Associação Nacional dos Centros de Pós Graduação em Economia [Brazilian Association of Graduate Programs in Economics],Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of financial economics, 5(2), 177-188.Xu, Y., Sherris, M., & Ziveyi, J. (2019). Market Price of Longevity Risk for a Multi‐Cohort Mortality Model With Application to Longevity Bond Option Pricing. Journal of Risk and Insurance. 描述 碩士
國立政治大學
風險管理與保險學系
107358026資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107358026 資料類型 thesis dc.contributor.advisor 謝明華 zh_TW dc.contributor.advisor Hsieh, Ming-Hua en_US dc.contributor.author (Authors) 陳文忠 zh_TW dc.contributor.author (Authors) Chen, Wen-Chung en_US dc.creator (作者) 陳文忠 zh_TW dc.creator (作者) Chen, Wen-Chung en_US dc.date (日期) 2020 en_US dc.date.accessioned 2-Sep-2020 11:51:18 (UTC+8) - dc.date.available 2-Sep-2020 11:51:18 (UTC+8) - dc.date.issued (上傳時間) 2-Sep-2020 11:51:18 (UTC+8) - dc.identifier (Other Identifiers) G0107358026 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/131516 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 風險管理與保險學系 zh_TW dc.description (描述) 107358026 zh_TW dc.description.abstract (摘要) Arbitrage Free Nelson Siegel model (AFNS model) 為滿足無套利條件且具優良配適與預測能力之利率模型，本研究探討 AFNS model 參數之校準方法。文中以台灣公債利率資料與美國公債利率資料為例，使用兩種不同的方式，搭配最小平方法與 Nelder-Mead 方法來校準參數，並比較其計算結果之差異。本文發現第二種參數校準方式可以有效率且準確地找出參數校準值。 zh_TW dc.description.abstract (摘要) Arbitrage-Free Nelson Siegel models is an affine term structure model that satisfies no-arbitrage condition and displays good fit and superior forecasting performance. This study explores the calibration method of AFNS model parameters. In this paper, the interest rate data of Taiwan government bonds and US government bonds are used as examples. Two methods are used, combined with the least square method and the Nelder-Mead method to calibrate the parameters, and the differences in the calculation results are compared. This article found that the second calibration method can efficiently and accurately find the parameter calibration value. en_US dc.description.tableofcontents 第一章 緒論...................................................... 7一、 研究背景與動機 .............................................. 7二、 研究目的.................................................... 8三、 利率名詞簡介 ............................................... 8四、 研究架構.................................................... 10第二章 文獻回顧.................................................. 11一、 利率模型介紹 ............................................... 11二、 最佳化方法 ................................................. 16第三章 研究方法.................................................. 18一、 參數校準方法 ............................................... 18二、 起始值決定方法.............................................. 20第四章 數值結果與分析 ............................................ 23一、 資料來源.................................................... 23二、 參數校準結果 ............................................... 24三、 市價與模型價之比較............................................ 27第五章 結論....................................................... 30參考資料 ......................................................... 31 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107358026 en_US dc.subject (關鍵詞) 利率期限模型 zh_TW dc.subject (關鍵詞) 參數校準 zh_TW dc.subject (關鍵詞) AFNS 模型 zh_TW dc.subject (關鍵詞) Nelder-Mead 方法 zh_TW dc.subject (關鍵詞) Term Structure Model en_US dc.subject (關鍵詞) Calibration en_US dc.subject (關鍵詞) AFNS model en_US dc.subject (關鍵詞) Nelder-Mead en_US dc.title (題名) 仿射AFNS利率模型參數之校準方法探討 zh_TW dc.title (題名) Calibrating the arbitrage-free Nelson-Siegel model en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.Christensen, J. H., Diebold, F. X., & Rudebusch, G. D. (2011). The affine arbitragefree class of Nelson–Siegel term structure models. Journal of Econometrics, 164(1), 4-20.Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (2005). A theory of the term structure of interest rates. In Theory of Valuation (pp. 129-164). World Scientific.Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. Journal of econometrics, 130(2), 337-364.Duffee, G. R. (2002). Term premia and interest rate forecasts in affine models. The Journal of Finance, 57(1), 405-443.Duffie, D., & Kan, R. (1996). A yield‐factor model of interest rates. Mathematical finance, 6(4), 379-406.Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica: Journal of the Econometric Society, 77-105.Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The review of financial studies, 3(4), 573-592.IAIS, ICS, Retrieved June 1 2020, from: https://www.iaisweb.org/page/supervisorymaterial/insurance-capital-standardMarek, J. (2015). The Nelson-Siegel Model: Present Application and Alternative Lambda Determination.Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The computer journal, 7(4), 308-313.Nelson, C. R., & Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of business, 473-489.Singleton, K. J. (2009). Empirical dynamic asset pricing: model specification and econometric assessment. Princeton University Press.Tourrucôo, F., Caldeira, J. F., Moura, G., & Santos, A. (2016). Forecasting the yield curve with the arbitrage-free dynamic Nelson–Siegel model: Brazilian evidence. Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting]. Niterói: ANPEC-Associação Nacional dos Centros de Pós Graduação em Economia [Brazilian Association of Graduate Programs in Economics],Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of financial economics, 5(2), 177-188.Xu, Y., Sherris, M., & Ziveyi, J. (2019). Market Price of Longevity Risk for a Multi‐Cohort Mortality Model With Application to Longevity Bond Option Pricing. Journal of Risk and Insurance. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202001669 en_US
