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題名 美國退休福利保險公司狀態轉換保險評價模型
The Pricing Model of Pension Benefit Guaranty Corporation Insurance with Regime Switching Processes
作者 王暐豪
Wang, Wei Hao
貢獻者 林士貴<br>蔡紋琦
Lin, Shih Kuei<br>Tsai, Wen Chi
王暐豪
Wang, Wei Hao
關鍵詞 美國退休福利保險公司(PBGC)
狀態轉換過程模型
EM 演算法
Pension Benefit Guaranty Corporation(PBGC)
Regime Switching Process
EM Algorithm
日期 2016
上傳時間 20-Jul-2016 16:52:38 (UTC+8)
摘要 本文研究美國退休福利保險公司(PBGC)保險價值的計算,延伸 Marcus (1987)模型,提出狀態轉換過程保險價值模型計算,也就是將市場分為兩種情況,正成長率視為正常狀態,負成長率為衰退狀態,利用狀態轉換過程評價 PBGC 契約在經濟困難而終止和介入終止下合理的保險價值。在參數估計方面,本文以 S&P500股價指數和一年期國庫券資料參數估計值及Marcus(1987)和Pennacchi and Lewis(1994)的方式給定參數,以 EM-PSO-Gradient 延伸 EM-Gradient 方法並以最大概似函數值、AIC 準則和 BIC 準則比較估計結果。最後固定其他參數, 探討狀態轉換過程保險價值模型對參數調整後保險價值的影響之敏感度分析。
In this paper, we evaluate Pension Benefit Guaranty Corporation insurance values through regime switching models, which is the extension of the models of Marcus (1987). That is, we can separate periods of economy with faster growth from those with slower growth when observing long-term trends in economy and calculate the reasonable PBGC insurance values under distress termination and intervention termination by regime switching processes. We set parameters by estimating S&P 500 index and 1-year treasury bills by EM-PSO-Gradient, which is the extensive method of EM-Gradient and refer the methods of setting parameters from Marcus (1987) and Pennacchi and Lewis (1994). After that, we compare the maximum likelihood estimates, AIC and BIC of the estimative results. Finally, we do sensitivity analysis through given the other parameters and look into what would impact on our models of insurance values when adjusting one parameter.
參考文獻 [1] Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6): 716-723.
[2] Black, F., & Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3): 637-654.
[3] Bodie, Z., Marcus, A. J., & Merton, R. C., 1988. Pensions in the U.S. Economy. University of Chicago Press.
[4] Dempster, A. P., Laird, N. M., & Rubin, D. B., 1977. Maximum likelihood from incomplete data via EM algorithm. Journal of the Royal Statistical Society. Series
B (Methodological), 39(1): 1-38.
[5] Ehiwario, J. C., & Aghamie, S. O., 2014. Comparative study of bisection, Newton-Raphson and secant methods of root-finding problems. IOSR Journal of Engineering, 4(4): 1-7.
[6] Hamilton, J. D., 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57: 357-384.
[7] Hsieh, S. J., Chen, A. H., & Ferris, K. R., 1994. The valuation of PBGC insurance premiums using an option pricing model. The Journal of Finance and
Quantitative Analysis, 29(1): 89-99.
[8] Jordan, M., & Jacobs, R. A., 1994. Hierarchical mixtures of experts and the EM
algorithm. Neural Computation, 6(2): 181-214.
[9] Karla, R., & Jain, G., 1997. A continuous-time model to determine the intervention policy for PBGC. Journal of Banking and Finance, 21: 1159-1177.
[10] Kennedy, J., & Eberhart, R., 1995. Neural Networks. Paper presented at Proceedings of IEEE International Conference.
[11]Lange, K., 1995. A quasi-newton acceleration of the EM algorithm. Statistica Sinica, 5: 1-18.
[12] Lee, J. P., & Yu, M. T., 2006. Closure rules and the valuation of pension benefit guaranty. Paper presented at Financial Management Association Annual Meeting,
Salt Lake City U.S.A.
[13] Marcus, A. J., 1987. Corporate pension policy and the value of PBGC insurance, in Bodie, Z., J. Shoven, and D. A. Wise (Eds), Issues in Pension Economics, University of Chicago Press: 49-79.
[14] Pension benefit guaranty corporation, 2013. Pension Insurance Data Book. [15] Pension benefit guaranty corporation, 2013. PBGC FY 2013 Projections Report.
[16] Pennacchi, G. G., & Lewis, C. M., 1994. The value of pension benefit guaranty
corporation insurance. Journal of Money, Credit and Banking, 26(3), Part 2: Federal Credit Allocation: Theory, Evidence, and History: 735-753.
[17]Schwarz, G., 1978. Estimating the dimension of a model. Annals of Statistics, 6(2): 461-464.
描述 碩士
國立政治大學
統計學系
103354024
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103354024
資料類型 thesis
dc.contributor.advisor 林士貴<br>蔡紋琦zh_TW
dc.contributor.advisor Lin, Shih Kuei<br>Tsai, Wen Chien_US
dc.contributor.author (Authors) 王暐豪zh_TW
dc.contributor.author (Authors) Wang, Wei Haoen_US
dc.creator (作者) 王暐豪zh_TW
dc.creator (作者) Wang, Wei Haoen_US
dc.date (日期) 2016en_US
dc.date.accessioned 20-Jul-2016 16:52:38 (UTC+8)-
dc.date.available 20-Jul-2016 16:52:38 (UTC+8)-
dc.date.issued (上傳時間) 20-Jul-2016 16:52:38 (UTC+8)-
dc.identifier (Other Identifiers) G0103354024en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99313-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 103354024zh_TW
dc.description.abstract (摘要) 本文研究美國退休福利保險公司(PBGC)保險價值的計算,延伸 Marcus (1987)模型,提出狀態轉換過程保險價值模型計算,也就是將市場分為兩種情況,正成長率視為正常狀態,負成長率為衰退狀態,利用狀態轉換過程評價 PBGC 契約在經濟困難而終止和介入終止下合理的保險價值。在參數估計方面,本文以 S&P500股價指數和一年期國庫券資料參數估計值及Marcus(1987)和Pennacchi and Lewis(1994)的方式給定參數,以 EM-PSO-Gradient 延伸 EM-Gradient 方法並以最大概似函數值、AIC 準則和 BIC 準則比較估計結果。最後固定其他參數, 探討狀態轉換過程保險價值模型對參數調整後保險價值的影響之敏感度分析。zh_TW
dc.description.abstract (摘要) In this paper, we evaluate Pension Benefit Guaranty Corporation insurance values through regime switching models, which is the extension of the models of Marcus (1987). That is, we can separate periods of economy with faster growth from those with slower growth when observing long-term trends in economy and calculate the reasonable PBGC insurance values under distress termination and intervention termination by regime switching processes. We set parameters by estimating S&P 500 index and 1-year treasury bills by EM-PSO-Gradient, which is the extensive method of EM-Gradient and refer the methods of setting parameters from Marcus (1987) and Pennacchi and Lewis (1994). After that, we compare the maximum likelihood estimates, AIC and BIC of the estimative results. Finally, we do sensitivity analysis through given the other parameters and look into what would impact on our models of insurance values when adjusting one parameter.en_US
dc.description.tableofcontents 第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 4
1.3 本文架構 5
第二章 文獻回顧 6
2.1 退休金模型 6
2.2 資產動態模型 9
2.3 最大期望演算法 10
2.4 最佳化演算法 10
第三章 契約介紹 12
3.1 PBGC 資金來源12
3.2 PBGC 終止形式 12
3.2.1 一般終止(Standard Termination) 12
3.2.2 經濟困難而終止(Distress Termination) 13
3.2.3 介入終止(Intervention Termination)13
第四章 狀態轉換模型下之退休金評價 15
4.1 狀態轉換模型下之動態過程 15
4.1.1 狀態轉換下退休準備金動態過程 15
4.1.2 應計福利過程(Accrued Benefit Dynamics) 16
4.1.3 狀態轉換下公司資產之公允價值與公司負債動態過程 16
4.1.4 狀態轉換下利率與退休準備金二維動態過程 17
4.1.5 狀態轉換下利率與應計福利二維動態過程 18
4.1.6 狀態轉換下利率與公司資產之公允價值和利率與公司負債動態過程19
4.2 測度轉換 20
4.2.1 風險中立機率測度之狀態轉換下退休準備金之動態過程 20
4.2.2 風險中立機率測度下應計福利之動態過程 21
4.2.3 風險中立機率測度之狀態轉換下公司資產之公允價值和公司負債之動態過程 22
4.2.4 遠期機率測度之狀態轉換下退休準備金之動態過程 24
4.2.5 遠期機率測度之應計福利之動態過程 25
4.2.6 遠期機率測度之狀態轉換下公司資產之公允價值和公司負債之動態過程 26
4.3 狀態轉換模型下之退休金評價 27
4.3.1 狀態轉換下經濟困難而終止保險價值 28
4.3.2 狀態轉換下介入終止保險價值 29
第五章 狀態轉換模型之估計與選取 31
5.1 模型介紹 31
5.2 參數估計 33
5.2.1 EM-Gradient 演算法下之最大期望估計法 36
5.2.2 EM-PSO-Gradient 演算法下之最大期望估計法 37
5.3 模型選取 38
第六章 實證與敏感度分析 40
6.1 資料來源 40
6.2 參數估計結果 41
6.3 敏感度分析 42
第七章 結論 44
參考文獻 45
附錄 47
附錄A 狀態轉換下經濟困難而終止保險價值 47
附錄B 狀態轉換下介入終止保險評價 51
附錄C 隨機利率之狀態轉換下經濟困難而終止保險評價 54
附錄D 隨機利率之狀態轉換下介入終止保險評價 57		zh_TW
dc.format.extent 1587488 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354024en_US
dc.subject (關鍵詞) 美國退休福利保險公司(PBGC)zh_TW
dc.subject (關鍵詞) 狀態轉換過程模型zh_TW
dc.subject (關鍵詞) EM 演算法zh_TW
dc.subject (關鍵詞) Pension Benefit Guaranty Corporation(PBGC)en_US
dc.subject (關鍵詞) Regime Switching Processen_US
dc.subject (關鍵詞) EM Algorithmen_US
dc.title (題名) 美國退休福利保險公司狀態轉換保險評價模型zh_TW
dc.title (題名) The Pricing Model of Pension Benefit Guaranty Corporation Insurance with Regime Switching Processesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6): 716-723.
[2] Black, F., & Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3): 637-654.
[3] Bodie, Z., Marcus, A. J., & Merton, R. C., 1988. Pensions in the U.S. Economy. University of Chicago Press.
[4] Dempster, A. P., Laird, N. M., & Rubin, D. B., 1977. Maximum likelihood from incomplete data via EM algorithm. Journal of the Royal Statistical Society. Series
B (Methodological), 39(1): 1-38.
[5] Ehiwario, J. C., & Aghamie, S. O., 2014. Comparative study of bisection, Newton-Raphson and secant methods of root-finding problems. IOSR Journal of Engineering, 4(4): 1-7.
[6] Hamilton, J. D., 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57: 357-384.
[7] Hsieh, S. J., Chen, A. H., & Ferris, K. R., 1994. The valuation of PBGC insurance premiums using an option pricing model. The Journal of Finance and
Quantitative Analysis, 29(1): 89-99.
[8] Jordan, M., & Jacobs, R. A., 1994. Hierarchical mixtures of experts and the EM
algorithm. Neural Computation, 6(2): 181-214.
[9] Karla, R., & Jain, G., 1997. A continuous-time model to determine the intervention policy for PBGC. Journal of Banking and Finance, 21: 1159-1177.
[10] Kennedy, J., & Eberhart, R., 1995. Neural Networks. Paper presented at Proceedings of IEEE International Conference.
[11]Lange, K., 1995. A quasi-newton acceleration of the EM algorithm. Statistica Sinica, 5: 1-18.
[12] Lee, J. P., & Yu, M. T., 2006. Closure rules and the valuation of pension benefit guaranty. Paper presented at Financial Management Association Annual Meeting,
Salt Lake City U.S.A.
[13] Marcus, A. J., 1987. Corporate pension policy and the value of PBGC insurance, in Bodie, Z., J. Shoven, and D. A. Wise (Eds), Issues in Pension Economics, University of Chicago Press: 49-79.
[14] Pension benefit guaranty corporation, 2013. Pension Insurance Data Book. [15] Pension benefit guaranty corporation, 2013. PBGC FY 2013 Projections Report.
[16] Pennacchi, G. G., & Lewis, C. M., 1994. The value of pension benefit guaranty
corporation insurance. Journal of Money, Credit and Banking, 26(3), Part 2: Federal Credit Allocation: Theory, Evidence, and History: 735-753.
[17]Schwarz, G., 1978. Estimating the dimension of a model. Annals of Statistics, 6(2): 461-464.		zh_TW