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題名 評價連結隨機保證報酬率之保證價值
Pricing guarantees linked to stochastic guaranteed rates of return作者 謝宗佑 貢獻者 陳松男
謝宗佑關鍵詞 利率保證
LIBOR 市場模型
確定提撥制退休金計畫
Interest rate guarantee
LIBOR market mode
Defined contribution pension plans日期 2010 上傳時間 27-Jun-2013 16:41:48 (UTC+8) 摘要 本文採用LIBOR市場利率模型評價確定提撥制退休金計畫所附之收益率保證，此保證收益率連結至隨機LIBOR市場利率，在相關的文獻上(特別在隨機利率方面)，尚未有相關的研究。本文同時考慮兩種保證型態：到期日保證與多期保證，運用平賭過程理論，在延伸之LIBOR市場利率模型(ELMM)下推導此兩種保證的理論公式解。相較於其他利率模型或HJM模型，採用ELMM所推得之評價公式更適合於實務運用。為供實務運用，文中並探討如何進行參數校準，亦進行蒙地卡羅模擬以驗證模型理論解的準確性。
We derive the pricing formulas for the guarantees embedded in defined contribution (DC) pension plans with the guaranteed minimum rate of return set relative to a LIBOR interest rate. The guaranteed rate associated with a stochastic LIBOR interest rate has not yet been studiedin the relevant literature, particularly in the presence of stochastic interest rates. An extended LIBOR market model (LMM) is employed to price the interest rate guarantees embedded in DC pension plans under maturity and multi-period guarantees. The pricing formulas derived underthe extended LMM are more tractable and feasible for practice than those derived under the instantaneous short rate models or the HJM model. Calibration procedures are also discussed for practical implementation. Monte Carlo simulation is provided to evaluate the accuracy of the theoretical results.參考文獻 Amin, K.I., Jarrow, R., 1991. Pricing Foreign Currency Options under Stochastic Interest Rates. Journal of International Money and Finance 10, 310-329.Bakken, H., Lindset, S., Olson, L. H., 2006. Pricing of Multi-period Rate of Return Guarantees: The Monte Carlo Approach. Insurance: Mathematics and Economics 39, 135-149.Black, F., 1976. The Pricing of Commodity Contracts. Journal of Financial Economics 3,167-179.Brace, A., Dun, T.A., Barton, G., 1998. Towards a Central.Interest Rate Model. Paper presented at the Conference Global Derivatives’98.Brace, A., Gatarek, D., Musiela, M., 1997. The Market Model of Interest Rate Dynamics. Mathematical Finance 7, 127-147.Brace, A., Womersley, R.S., 2000. Exact Fit to the Swaption Volatility Matrix Using Semidefinite Programming. Paper presented at the ICBI Global Derivatives Conference.Boyle, P. P., Hardy, M. R., 1997. Reserving for Maturity Guarantees: Two Approaches. Insurance: Mathematics and Economics 21, 113-127.Boyle, P. P., Schwartz, E. S., 1977. Equilibrium Prices of Guarantees under Equity-Linked Contracts. Journal of Risk and Insurance 44, 639-660.Brennan, J. M., Schwartz, E. S., 1976. The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics 3,195-213.Brigo, D., Mercurio, F., 2001. Interest Rate Models: Theory and Practice. Springer Verlag, 39 Heidelberg. Continuous Mortality Investigation Bureau., 1999. Standard Tables of Mortality Based on the 1991-1994 Experiences. Continuous Mortality Investigation Report No. 17. The Institute and Faculty of Actuaries, UK.Cox, J.C., Ingersoll J.E., Ross, S.A., 1985. A Theory of the Term Structure of Interest Rates. Econometrica 53, 385-407.Duffie, D., 1988. Security Markets: Stochastic Models. Academic Press, Boston.Ekern, S., Persson, S. A., 1996. Exotic Unit-Linked Life Insurance Contracts. The GENEVA Papers on Risk and Insurance Theory 21, 35-63.Grosen, A., Jorgensen, P. L., 1997. Valuation of Early Exercisable Interest Rate Guarantees. Journal of Risk and Insurance 64, 481-503.Grosen, A., Jorgensen, P. L., 2000. Fair Valuation of Life Insurance Liabilities: The Impact of Interest Rate Guarantees, Surrender Options, and Bonus Policies. Insurance: Mathematics and Economics 26, 37-57.Hansen, M., Miltersen, K. R., 2002. Minimum Rate of Return Guarantees: the Danish Case. Scandinavian Actuarial Journal 4, 280-318.Heath, D., Jarrow, R., Morton A., 1992. Bond Pricing and the Term Structure of Interest Rates: a New Methodology for Contingent Claims Valuation. Econometrica 60, 77-105.Hull, J., 2003. Options, Futures and Other Derivatives (5th ed.). Prentice Hall, New Jersey.Lindset, S., 2003. Pricing of Multi-period Rate of Return Guarantees. Insurance: Mathematics and Economics 33, 629-644.Lindset, S., 2004. Relative Guarantees. The Geneva Papers on Risk and Insurance Theory 29, 187-209.Margrabe, W., 1978. The Value of an Option to Exchange One Asset for Another. The Journal of Finance 33, 177-186.Miltersen, K. R., Persson, S. A., 1999. Pricing Rate of Return Guarantee in a Heath-Jarrow-Morton Framework. Insurance: Mathematics and Economics 25, 307-325.Miltersen, K. R., Sandmann, K., Sondermann, D., 1997. Closed Form Solutions for Term Structure Derivatives with Log-normal Interest Rates. The Journal of Finance 52, 409-430.Musiela, M., Rutkowski, M., 1997. Continuous-time Term Structure Model: Forward Measure Approach. Finance and Stochastics 4, 261-292.Musiela, M., Rutkowski, M., 2005. Martingale Methods in Financial Modelling (2nd ed.). Springer Verlag, Heidelberg.Pennacchi, G. G., 1999. The Value of Guarantees on Pension Fund Returns. Journal of Risk and Insurance 66, 219-237.Persson, S. A., Aase, K. K., 1997. Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products. Journal of Risk and Insurance 64, 599-617.Rebonato, R., 1999. On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix. The Journal of Computational Finance 2, 5-27.Rogers, C., 1996. Gaussian Errors. Risk 9, 42-45. Schl¨ogl, E., 2002. A Multicurrency Extension of the Lognormal Interest Rate Market Models. Finance and Stochastics 6, 173-188.Svoboda, S., 2004. Interest Rate Modelling. Palgrave Macmillan. Vasicek, O., 1977. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5, 177-188.Walker, K. L., 1992. Guaranteed Investment Contracts: Risk Analysis and Portfolio Strategies. Business One Irwin, Illinois.Wu, T. P., Chen, S. N., 2007a. Equity Swaps in a LIBOR Market Model. Journal of Futures Markets 27, 893-920.Wu, T. P., Chen, S. N., 2007b. Cross-currency Equity Swaps with the BGM Model. Journal of Derivatives, Winter, 60-76.Yang, S. S., Yueh, M. L., Tang, C. H., 2008. Valuation of the Interest Rate Guarantee Embedded in Defined Contribution Pension Plans. Insurance: Mathematics and Economics 42, 920-934. 描述 博士
國立政治大學
金融研究所
93352503
99資料來源 http://thesis.lib.nccu.edu.tw/record/#G0933525031 資料類型 thesis dc.contributor.advisor 陳松男 zh_TW dc.contributor.author (Authors) 謝宗佑 zh_TW dc.creator (作者) 謝宗佑 zh_TW dc.date (日期) 2010 en_US dc.date.accessioned 27-Jun-2013 16:41:48 (UTC+8) - dc.date.available 27-Jun-2013 16:41:48 (UTC+8) - dc.date.issued (上傳時間) 27-Jun-2013 16:41:48 (UTC+8) - dc.identifier (Other Identifiers) G0933525031 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58586 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融研究所 zh_TW dc.description (描述) 93352503 zh_TW dc.description (描述) 99 zh_TW dc.description.abstract (摘要) 本文採用LIBOR市場利率模型評價確定提撥制退休金計畫所附之收益率保證，此保證收益率連結至隨機LIBOR市場利率，在相關的文獻上(特別在隨機利率方面)，尚未有相關的研究。本文同時考慮兩種保證型態：到期日保證與多期保證，運用平賭過程理論，在延伸之LIBOR市場利率模型(ELMM)下推導此兩種保證的理論公式解。相較於其他利率模型或HJM模型，採用ELMM所推得之評價公式更適合於實務運用。為供實務運用，文中並探討如何進行參數校準，亦進行蒙地卡羅模擬以驗證模型理論解的準確性。 zh_TW dc.description.abstract (摘要) We derive the pricing formulas for the guarantees embedded in defined contribution (DC) pension plans with the guaranteed minimum rate of return set relative to a LIBOR interest rate. The guaranteed rate associated with a stochastic LIBOR interest rate has not yet been studiedin the relevant literature, particularly in the presence of stochastic interest rates. An extended LIBOR market model (LMM) is employed to price the interest rate guarantees embedded in DC pension plans under maturity and multi-period guarantees. The pricing formulas derived underthe extended LMM are more tractable and feasible for practice than those derived under the instantaneous short rate models or the HJM model. Calibration procedures are also discussed for practical implementation. Monte Carlo simulation is provided to evaluate the accuracy of the theoretical results. en_US dc.description.tableofcontents 1 Introduction 32 Guarantees and Economic Model 82.1 DC plans with Guarantees 82.2 LIBOR Market Model (LMM) 102.3 The Extended LIBOR Market Model 133 Valuation of Relative Interest Rate Guarantees 163.1 Valuation of the First-Type Guarantee (Maturity Guarantee) 163.2 Valuation of the Second-Type Guarantee (Multi-Period Guarantee) 194 Calibration Procedure and Numerical Examples 214.1 Calibration Procedure 214.2 Numerical Analysis 235 Conclusions 26Appendix A: Proof of Theorem 3.1 27Appendix B: Proof of Theorem 3.2 34Bibliography 39 zh_TW dc.format.extent 2618392 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0933525031 en_US dc.subject (關鍵詞) 利率保證 zh_TW dc.subject (關鍵詞) LIBOR 市場模型 zh_TW dc.subject (關鍵詞) 確定提撥制退休金計畫 zh_TW dc.subject (關鍵詞) Interest rate guarantee en_US dc.subject (關鍵詞) LIBOR market mode en_US dc.subject (關鍵詞) Defined contribution pension plans en_US dc.title (題名) 評價連結隨機保證報酬率之保證價值 zh_TW dc.title (題名) Pricing guarantees linked to stochastic guaranteed rates of return en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Amin, K.I., Jarrow, R., 1991. Pricing Foreign Currency Options under Stochastic Interest Rates. Journal of International Money and Finance 10, 310-329.Bakken, H., Lindset, S., Olson, L. H., 2006. Pricing of Multi-period Rate of Return Guarantees: The Monte Carlo Approach. Insurance: Mathematics and Economics 39, 135-149.Black, F., 1976. The Pricing of Commodity Contracts. Journal of Financial Economics 3,167-179.Brace, A., Dun, T.A., Barton, G., 1998. Towards a Central.Interest Rate Model. Paper presented at the Conference Global Derivatives’98.Brace, A., Gatarek, D., Musiela, M., 1997. The Market Model of Interest Rate Dynamics. Mathematical Finance 7, 127-147.Brace, A., Womersley, R.S., 2000. Exact Fit to the Swaption Volatility Matrix Using Semidefinite Programming. Paper presented at the ICBI Global Derivatives Conference.Boyle, P. P., Hardy, M. R., 1997. Reserving for Maturity Guarantees: Two Approaches. Insurance: Mathematics and Economics 21, 113-127.Boyle, P. P., Schwartz, E. S., 1977. Equilibrium Prices of Guarantees under Equity-Linked Contracts. Journal of Risk and Insurance 44, 639-660.Brennan, J. M., Schwartz, E. S., 1976. The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics 3,195-213.Brigo, D., Mercurio, F., 2001. Interest Rate Models: Theory and Practice. Springer Verlag, 39 Heidelberg. Continuous Mortality Investigation Bureau., 1999. Standard Tables of Mortality Based on the 1991-1994 Experiences. Continuous Mortality Investigation Report No. 17. The Institute and Faculty of Actuaries, UK.Cox, J.C., Ingersoll J.E., Ross, S.A., 1985. A Theory of the Term Structure of Interest Rates. Econometrica 53, 385-407.Duffie, D., 1988. Security Markets: Stochastic Models. Academic Press, Boston.Ekern, S., Persson, S. A., 1996. Exotic Unit-Linked Life Insurance Contracts. The GENEVA Papers on Risk and Insurance Theory 21, 35-63.Grosen, A., Jorgensen, P. L., 1997. Valuation of Early Exercisable Interest Rate Guarantees. Journal of Risk and Insurance 64, 481-503.Grosen, A., Jorgensen, P. L., 2000. Fair Valuation of Life Insurance Liabilities: The Impact of Interest Rate Guarantees, Surrender Options, and Bonus Policies. Insurance: Mathematics and Economics 26, 37-57.Hansen, M., Miltersen, K. R., 2002. Minimum Rate of Return Guarantees: the Danish Case. Scandinavian Actuarial Journal 4, 280-318.Heath, D., Jarrow, R., Morton A., 1992. Bond Pricing and the Term Structure of Interest Rates: a New Methodology for Contingent Claims Valuation. Econometrica 60, 77-105.Hull, J., 2003. Options, Futures and Other Derivatives (5th ed.). Prentice Hall, New Jersey.Lindset, S., 2003. Pricing of Multi-period Rate of Return Guarantees. Insurance: Mathematics and Economics 33, 629-644.Lindset, S., 2004. Relative Guarantees. The Geneva Papers on Risk and Insurance Theory 29, 187-209.Margrabe, W., 1978. The Value of an Option to Exchange One Asset for Another. The Journal of Finance 33, 177-186.Miltersen, K. R., Persson, S. A., 1999. Pricing Rate of Return Guarantee in a Heath-Jarrow-Morton Framework. Insurance: Mathematics and Economics 25, 307-325.Miltersen, K. R., Sandmann, K., Sondermann, D., 1997. Closed Form Solutions for Term Structure Derivatives with Log-normal Interest Rates. The Journal of Finance 52, 409-430.Musiela, M., Rutkowski, M., 1997. Continuous-time Term Structure Model: Forward Measure Approach. Finance and Stochastics 4, 261-292.Musiela, M., Rutkowski, M., 2005. Martingale Methods in Financial Modelling (2nd ed.). Springer Verlag, Heidelberg.Pennacchi, G. G., 1999. The Value of Guarantees on Pension Fund Returns. Journal of Risk and Insurance 66, 219-237.Persson, S. A., Aase, K. K., 1997. Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products. Journal of Risk and Insurance 64, 599-617.Rebonato, R., 1999. On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix. The Journal of Computational Finance 2, 5-27.Rogers, C., 1996. Gaussian Errors. Risk 9, 42-45. Schl¨ogl, E., 2002. A Multicurrency Extension of the Lognormal Interest Rate Market Models. Finance and Stochastics 6, 173-188.Svoboda, S., 2004. Interest Rate Modelling. Palgrave Macmillan. Vasicek, O., 1977. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5, 177-188.Walker, K. L., 1992. Guaranteed Investment Contracts: Risk Analysis and Portfolio Strategies. Business One Irwin, Illinois.Wu, T. P., Chen, S. N., 2007a. Equity Swaps in a LIBOR Market Model. Journal of Futures Markets 27, 893-920.Wu, T. P., Chen, S. N., 2007b. Cross-currency Equity Swaps with the BGM Model. Journal of Derivatives, Winter, 60-76.Yang, S. S., Yueh, M. L., Tang, C. H., 2008. Valuation of the Interest Rate Guarantee Embedded in Defined Contribution Pension Plans. Insurance: Mathematics and Economics 42, 920-934. zh_TW
