學術產出-Theses

題名 縮減式模型下房屋抵押貸款之評價
Mortgage Valuation under Reduced-Form Model
作者 江淑玲
Chiang,Shu Ling
貢獻者 廖四郎
Liao,Szu Lang
江淑玲
Chiang,Shu Ling
關鍵詞 評價
房屋抵押貸款
提前清償
違約
縮減式模型
valuation
mortgage
prepayment risk
default risk
reduced-form approach
日期 2006
上傳時間 18-Sep-2009 20:17:13 (UTC+8)
摘要 房屋抵押貸款的評價,因為需考慮到貸款人的提前清償及違約風險造成現金流量之不確定性,決定房屋抵押貸款的價格比決定一般違約證券的價格更具困難度。因此,如何合理評估抵押貸款證券的價值實為一值得深入探討之課題,本文即針對此議題進行研究。傳統文獻在進行房屋抵押貸款的評價方法,主要可區分為兩種:結構模型(structural-form approach)及縮減式模型(reduced-form approach)。目前的文獻上,其評價的封閉解只存在於結構式模型,但在此模型下的評價,存在著違約與提前清償條件的設定問題,這將對評價的準確性造成很大的影響,在實務的應用上有一定的限制。再者,結構式模型在處理多變數且變數間具相關性的情況,存在一定的複雜性與困難度,而縮減式模型在此情況的處理上是較容易的。本研究將從縮減式模型的角度,引入 Jarrow (2001)的概念,在包含多重變數並考慮變數間相關係數之縮減模型下,進行房屋抵押貸款封閉解的推導。透過此方法可協助資產管理者從事投資組合配置最適化與避險策略的分析,亦期望能提供實務界一個更具可行性與效率性之房屋抵押貸款評價模型。
Valuing mortgage-related securities is more complicated than valuing regular defaultable claims due to the borrower’s prepayment behavior as well as the possibility of default. In general, the methods that are applied to investigate mortgage value and termination risk can be divided into two categories: a structural-form approach and a reduced-form approach. Some researchers use a structural-form model to obtain the closed-form formulae for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise and deal with the situation including multivariable and their correlations correlation among variables. As an alternative, the reduced-form model developed in this study is able to value the mortgage without setting boundary conditions, and can thereby accurately handle the multi-dimensional space of correlated state variables. This study extends Jarrow’s (2001) model to examine mortgage valuations. The purpose of this article is to derive a closed-form solution of the mortgage valuation equation under a general reduced-form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses, and makes it possible to more accurately and efficiently value the complicated mortgage.
參考文獻 Adams, K. and D. Van Deventer. 1994. Fitting Yield Curves and Forward Rate Curves with Maximum Smoothness. Journal of Fixed Income 4(1): 52-62.
Ambrose, B. W. and R. J. Buttimer. 2000. Embedded Options in the Mortgage Contract. Journal of Real Estate Finance and Economics 21(2): 95-111.
Ambrose, B. W. and A. B. Sanders. 2003. Commercial Mortgage-Backed Securities: Prepayment and Default. Journal of Real Estate Finance and Economics 26(2/3): 179-196.
Azevedo-Pereira, J. A., D. P. Newton and D. A. Paxson. 2003. Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation. Journal of Real Estate Finance and Economics 26(2/3): 197-221.
Bielecki, T. R. and M. Rutkowski. 2001. Credit Risk: Modeling, Valuation and Hedging. Berlin : Springer New York.
Black, F. and J. C. Cox. 1976. Valuing Corporate Securities: Some Effects of Bond Indenture Provisions. Journal of Finance 31: 351-367.
Calem, P. S. and M. LaCour-Little. 2004. Risked-Based Requirements for Mortgage Loans. Journal of Banking and Finance 28: 647-672.
Capone, Jr. C. A.. 2003. The FHA Budget Subsidy Simulation System: A Dynamic Simulation Model of Budget Outcomes for FHA Single-Family Mortgage Insurance. Technical Paper Series Congressional Budget Office.
Capozza, D. R., D. Kazarian and T. A. Thomson. 1998. The Conditional Probability of Mortgage Default. Real Estate Economics 26(3): 359-389.
Chen, R. R. and T. T. Yang. 1995. The Relevance of Interest Rate Process in Pricing Mortgage-Backed securities. Journal of Housing Research 6(2): 315-332.
Ciochetti, B. A., Y. Deng, G. Lee, J. D. Shilling, R. Yao. 2003. A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias. Journal of Real Estate Finance and Economics 27(1): 5-23.
Clapp, J. M., G.. M. Goldberg, J. P. Harding and M. LaCour-Little. 2001. Movers and Shuckers: Interdependent Prepayment Decisions. Real Estate Economics 29(3): 411-450.
Collin-Dufresne, P. and J. P. Harding. 1999. A Closed Form Formula for Valuing Mortgages. Journal of Real Estate Finance and Economics 19(2): 133-146.
Cox, D. R. and D. Oakes. 1984. Analysis of Survival Data. London: Chapman and Hall.
Deng, Y., J. M. Quigley and R. Van Order. 1996. Mortgage Default and Low Downpayment Loans: The Costs of Public Subsidy. Regional Science and Urban Economics 26: 263-285.
Driessen, J.. 2002. Is default event risk priced in corporate bond?. Working paper. University of American.
Duffee, G. R.. 1999. Estimating the Price Default Risk. The Review of Financial Studies 12(1): 197-226.
Frye, J.. 2000a. Collateral Damage. Risk 13(4): 91-94.
Frye, J.. 2000b. Depressing Recoveries. Risk 13(11): 108-111.
Goldberg, G. M. and J. P. Harding. 2003. Investment Characteristics of Low- and Moderate-Income Mortgage Loans. Journal of Housing Economics 12: 151-180.
Heath, D., R. Jarrow and A. Morton. 1992. Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation. Econometrica 60: 77-106.
Janosi, T., R. Jarrow and Y. Yildirim. 2003. Estimating Default Probabilities Implicit in Equity Price. Journal of Investment Management 1(1): 1-30.
Jarrow, R. , D. Lando and F. Yu. 2005. Default Risk and Diversification: Theory and Applications. Mathematical Finance 15(1): 1-26.
Jarrow, R. A. and S. M. Turnbull. 2000. The Intersection of Market and Credit Risk. Journal of Banking and Finance 24(1-2): 271-299.
Jarrow, R. and S. M. Turnbull. 1995. Pricing Options on Financial Securities Subject to Default Risk. Journal of Finance 50: 481-523.
Jarrow, R.. 2001. Default Parameter Estimation Using Market Prices. Financial Analysts Journal 5: 74-92.
Jokivuolle, E. and S. Peura. 2003. A Model for Estimating Recovery Rates and Collateral Haircuts for Bank Loans. European Financial Management 9(3): 299–314.
Kaplan, E. L. and P. Meier. 1958. Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association 53: 457-481.
Kau, J. B., D. C. Keenan, W. J. Muller Ⅲ and J. F. Epperson. 1993. Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages. Journal of Business 66: 595-618.
Kau, J. B. and D. C. Keenan. 1995. An Overview of the Option-Theoretic Pricing of Mortgages. Journal of Housing Research 6(2): 217-244.
Lambrecht, B. M., W. R. M. Perraudin and S. Satchell. 2003. Mortgage Default and Possession Under Recourse: A Competing Hazards Approach. Journal of Money, Credit and Banking 35(3): 425-442.
Lancaster, Tony. 1992. The Econometric Analysis of Transition Data. New York: Cambridge University Press.
Lando, D.. 1998. On Cox Processes and Credit Risky Securities. Review of Derivatives Research 2: 99-120.
Leland, H. E.. 1994. Corporate Debt Value, Bond Covenants, and Optimal Capital Structure. Journal of Finance 49: 1213-1252.
Merton, R.. 1974. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance 29: 449-470.
Miltersen, K. R., K. Sandmann, D. Sondermann. 1997. Close Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates. The Journal of Finance 52(1): 409-430.
Quigley, J. and R. Van Order. 1990. Efficiency in the Mortgage Market: The Borrower’s Perspective. AREUEA Journal 18(3): 237-252.
Quigley, J. and R. Van Order. 1995. Explicit Tests of Contingent Models of Mortgage Default. Journal of Real Estate Finance and Economics 11(2): 99-117.
Schwartz, E. S. and W. N. Torous. 1989. Prepayment and the Valuation of Mortgage-Backed Securities. Journal of Finance 44(2): 375-392.
Schwartz, E. S. and W. N. Torous. 1993. Mortgage Prepayment and Default Decisions: A Poisson Regression Approach. AREUEA Journal 21(4): 431-449.
Stanton, R. 1995. Rational Prepayment and the Valuation of Mortgage-Backed Securities. Review of Financial Studies 8. 677–708.
Vasicek, O.. 1977. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5: 177-188.
Yang, T. T., H. Buist and I. F. Megbolugbe. 1998. An Analysis of the Ex Ante Probabilities of Mortgage Prepayment and Default. Real Estate Economics 26(4): 651-676.
描述 博士
國立政治大學
金融研究所
91352503
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0913525031
資料類型 thesis
dc.contributor.advisor 廖四郎zh_TW
dc.contributor.advisor Liao,Szu Langen_US
dc.contributor.author (Authors) 江淑玲zh_TW
dc.contributor.author (Authors) Chiang,Shu Lingen_US
dc.creator (作者) 江淑玲zh_TW
dc.creator (作者) Chiang,Shu Lingen_US
dc.date (日期) 2006en_US
dc.date.accessioned 18-Sep-2009 20:17:13 (UTC+8)-
dc.date.available 18-Sep-2009 20:17:13 (UTC+8)-
dc.date.issued (上傳時間) 18-Sep-2009 20:17:13 (UTC+8)-
dc.identifier (Other Identifiers) G0913525031en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/36960-
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) 91352503zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) 房屋抵押貸款的評價,因為需考慮到貸款人的提前清償及違約風險造成現金流量之不確定性,決定房屋抵押貸款的價格比決定一般違約證券的價格更具困難度。因此,如何合理評估抵押貸款證券的價值實為一值得深入探討之課題,本文即針對此議題進行研究。傳統文獻在進行房屋抵押貸款的評價方法,主要可區分為兩種:結構模型(structural-form approach)及縮減式模型(reduced-form approach)。目前的文獻上,其評價的封閉解只存在於結構式模型,但在此模型下的評價,存在著違約與提前清償條件的設定問題,這將對評價的準確性造成很大的影響,在實務的應用上有一定的限制。再者,結構式模型在處理多變數且變數間具相關性的情況,存在一定的複雜性與困難度,而縮減式模型在此情況的處理上是較容易的。本研究將從縮減式模型的角度,引入 Jarrow (2001)的概念,在包含多重變數並考慮變數間相關係數之縮減模型下,進行房屋抵押貸款封閉解的推導。透過此方法可協助資產管理者從事投資組合配置最適化與避險策略的分析,亦期望能提供實務界一個更具可行性與效率性之房屋抵押貸款評價模型。zh_TW
dc.description.abstract (摘要) Valuing mortgage-related securities is more complicated than valuing regular defaultable claims due to the borrower’s prepayment behavior as well as the possibility of default. In general, the methods that are applied to investigate mortgage value and termination risk can be divided into two categories: a structural-form approach and a reduced-form approach. Some researchers use a structural-form model to obtain the closed-form formulae for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise and deal with the situation including multivariable and their correlations correlation among variables. As an alternative, the reduced-form model developed in this study is able to value the mortgage without setting boundary conditions, and can thereby accurately handle the multi-dimensional space of correlated state variables. This study extends Jarrow’s (2001) model to examine mortgage valuations. The purpose of this article is to derive a closed-form solution of the mortgage valuation equation under a general reduced-form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses, and makes it possible to more accurately and efficiently value the complicated mortgage.en_US
dc.description.tableofcontents CHAPTER 1 INTRODUCTION 1

CHAPTER 2 LITERATURE REVIEW 6

CHAPTER 3 THE MODEL 9
3.1 MORTGAGE CONTRACT 9
3.2 MODEL STRUCTURE 9
3.3 SOME SPECIFICATIONS IN THE MODEL 12
3.4 RISK-NEUTRAL MORTGAGE VALUATION 17

CHAPTER 4 IMPLEMENTATION OF THE MODEL ……..22
4.1 THE ESTIMATION OF PARAMETERS 22
4.2 SENSITIVITY ANALYSES OF STATE VARIABLE’S PARAMETERS 25
4.3 NUMERICAL RESULTS 28

CHAPTER 5 CONCLUSION 34

BIBLIOGRAPHY 36
APPENDIX A 39
APPENDIX B 46
zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0913525031en_US
dc.subject (關鍵詞) 評價zh_TW
dc.subject (關鍵詞) 房屋抵押貸款zh_TW
dc.subject (關鍵詞) 提前清償zh_TW
dc.subject (關鍵詞) 違約zh_TW
dc.subject (關鍵詞) 縮減式模型zh_TW
dc.subject (關鍵詞) valuationen_US
dc.subject (關鍵詞) mortgageen_US
dc.subject (關鍵詞) prepayment risken_US
dc.subject (關鍵詞) default risken_US
dc.subject (關鍵詞) reduced-form approachen_US
dc.title (題名) 縮減式模型下房屋抵押貸款之評價zh_TW
dc.title (題名) Mortgage Valuation under Reduced-Form Modelen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Adams, K. and D. Van Deventer. 1994. Fitting Yield Curves and Forward Rate Curves with Maximum Smoothness. Journal of Fixed Income 4(1): 52-62.zh_TW
dc.relation.reference (參考文獻) Ambrose, B. W. and R. J. Buttimer. 2000. Embedded Options in the Mortgage Contract. Journal of Real Estate Finance and Economics 21(2): 95-111.zh_TW
dc.relation.reference (參考文獻) Ambrose, B. W. and A. B. Sanders. 2003. Commercial Mortgage-Backed Securities: Prepayment and Default. Journal of Real Estate Finance and Economics 26(2/3): 179-196.zh_TW
dc.relation.reference (參考文獻) Azevedo-Pereira, J. A., D. P. Newton and D. A. Paxson. 2003. Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation. Journal of Real Estate Finance and Economics 26(2/3): 197-221.zh_TW
dc.relation.reference (參考文獻) Bielecki, T. R. and M. Rutkowski. 2001. Credit Risk: Modeling, Valuation and Hedging. Berlin : Springer New York.zh_TW
dc.relation.reference (參考文獻) Black, F. and J. C. Cox. 1976. Valuing Corporate Securities: Some Effects of Bond Indenture Provisions. Journal of Finance 31: 351-367.zh_TW
dc.relation.reference (參考文獻) Calem, P. S. and M. LaCour-Little. 2004. Risked-Based Requirements for Mortgage Loans. Journal of Banking and Finance 28: 647-672.zh_TW
dc.relation.reference (參考文獻) Capone, Jr. C. A.. 2003. The FHA Budget Subsidy Simulation System: A Dynamic Simulation Model of Budget Outcomes for FHA Single-Family Mortgage Insurance. Technical Paper Series Congressional Budget Office.zh_TW
dc.relation.reference (參考文獻) Capozza, D. R., D. Kazarian and T. A. Thomson. 1998. The Conditional Probability of Mortgage Default. Real Estate Economics 26(3): 359-389.zh_TW
dc.relation.reference (參考文獻) Chen, R. R. and T. T. Yang. 1995. The Relevance of Interest Rate Process in Pricing Mortgage-Backed securities. Journal of Housing Research 6(2): 315-332.zh_TW
dc.relation.reference (參考文獻) Ciochetti, B. A., Y. Deng, G. Lee, J. D. Shilling, R. Yao. 2003. A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias. Journal of Real Estate Finance and Economics 27(1): 5-23.zh_TW
dc.relation.reference (參考文獻) Clapp, J. M., G.. M. Goldberg, J. P. Harding and M. LaCour-Little. 2001. Movers and Shuckers: Interdependent Prepayment Decisions. Real Estate Economics 29(3): 411-450.zh_TW
dc.relation.reference (參考文獻) Collin-Dufresne, P. and J. P. Harding. 1999. A Closed Form Formula for Valuing Mortgages. Journal of Real Estate Finance and Economics 19(2): 133-146.zh_TW
dc.relation.reference (參考文獻) Cox, D. R. and D. Oakes. 1984. Analysis of Survival Data. London: Chapman and Hall.zh_TW
dc.relation.reference (參考文獻) Deng, Y., J. M. Quigley and R. Van Order. 1996. Mortgage Default and Low Downpayment Loans: The Costs of Public Subsidy. Regional Science and Urban Economics 26: 263-285.zh_TW
dc.relation.reference (參考文獻) Driessen, J.. 2002. Is default event risk priced in corporate bond?. Working paper. University of American.zh_TW
dc.relation.reference (參考文獻) Duffee, G. R.. 1999. Estimating the Price Default Risk. The Review of Financial Studies 12(1): 197-226.zh_TW
dc.relation.reference (參考文獻) Frye, J.. 2000a. Collateral Damage. Risk 13(4): 91-94.zh_TW
dc.relation.reference (參考文獻) Frye, J.. 2000b. Depressing Recoveries. Risk 13(11): 108-111.zh_TW
dc.relation.reference (參考文獻) Goldberg, G. M. and J. P. Harding. 2003. Investment Characteristics of Low- and Moderate-Income Mortgage Loans. Journal of Housing Economics 12: 151-180.zh_TW
dc.relation.reference (參考文獻) Heath, D., R. Jarrow and A. Morton. 1992. Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation. Econometrica 60: 77-106.zh_TW
dc.relation.reference (參考文獻) Janosi, T., R. Jarrow and Y. Yildirim. 2003. Estimating Default Probabilities Implicit in Equity Price. Journal of Investment Management 1(1): 1-30.zh_TW
dc.relation.reference (參考文獻) Jarrow, R. , D. Lando and F. Yu. 2005. Default Risk and Diversification: Theory and Applications. Mathematical Finance 15(1): 1-26.zh_TW
dc.relation.reference (參考文獻) Jarrow, R. A. and S. M. Turnbull. 2000. The Intersection of Market and Credit Risk. Journal of Banking and Finance 24(1-2): 271-299.zh_TW
dc.relation.reference (參考文獻) Jarrow, R. and S. M. Turnbull. 1995. Pricing Options on Financial Securities Subject to Default Risk. Journal of Finance 50: 481-523.zh_TW
dc.relation.reference (參考文獻) Jarrow, R.. 2001. Default Parameter Estimation Using Market Prices. Financial Analysts Journal 5: 74-92.zh_TW
dc.relation.reference (參考文獻) Jokivuolle, E. and S. Peura. 2003. A Model for Estimating Recovery Rates and Collateral Haircuts for Bank Loans. European Financial Management 9(3): 299–314.zh_TW
dc.relation.reference (參考文獻) Kaplan, E. L. and P. Meier. 1958. Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association 53: 457-481.zh_TW
dc.relation.reference (參考文獻) Kau, J. B., D. C. Keenan, W. J. Muller Ⅲ and J. F. Epperson. 1993. Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages. Journal of Business 66: 595-618.zh_TW
dc.relation.reference (參考文獻) Kau, J. B. and D. C. Keenan. 1995. An Overview of the Option-Theoretic Pricing of Mortgages. Journal of Housing Research 6(2): 217-244.zh_TW
dc.relation.reference (參考文獻) Lambrecht, B. M., W. R. M. Perraudin and S. Satchell. 2003. Mortgage Default and Possession Under Recourse: A Competing Hazards Approach. Journal of Money, Credit and Banking 35(3): 425-442.zh_TW
dc.relation.reference (參考文獻) Lancaster, Tony. 1992. The Econometric Analysis of Transition Data. New York: Cambridge University Press.zh_TW
dc.relation.reference (參考文獻) Lando, D.. 1998. On Cox Processes and Credit Risky Securities. Review of Derivatives Research 2: 99-120.zh_TW
dc.relation.reference (參考文獻) Leland, H. E.. 1994. Corporate Debt Value, Bond Covenants, and Optimal Capital Structure. Journal of Finance 49: 1213-1252.zh_TW
dc.relation.reference (參考文獻) Merton, R.. 1974. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance 29: 449-470.zh_TW
dc.relation.reference (參考文獻) Miltersen, K. R., K. Sandmann, D. Sondermann. 1997. Close Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates. The Journal of Finance 52(1): 409-430.zh_TW
dc.relation.reference (參考文獻) Quigley, J. and R. Van Order. 1990. Efficiency in the Mortgage Market: The Borrower’s Perspective. AREUEA Journal 18(3): 237-252.zh_TW
dc.relation.reference (參考文獻) Quigley, J. and R. Van Order. 1995. Explicit Tests of Contingent Models of Mortgage Default. Journal of Real Estate Finance and Economics 11(2): 99-117.zh_TW
dc.relation.reference (參考文獻) Schwartz, E. S. and W. N. Torous. 1989. Prepayment and the Valuation of Mortgage-Backed Securities. Journal of Finance 44(2): 375-392.zh_TW
dc.relation.reference (參考文獻) Schwartz, E. S. and W. N. Torous. 1993. Mortgage Prepayment and Default Decisions: A Poisson Regression Approach. AREUEA Journal 21(4): 431-449.zh_TW
dc.relation.reference (參考文獻) Stanton, R. 1995. Rational Prepayment and the Valuation of Mortgage-Backed Securities. Review of Financial Studies 8. 677–708.zh_TW
dc.relation.reference (參考文獻) Vasicek, O.. 1977. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5: 177-188.zh_TW
dc.relation.reference (參考文獻) Yang, T. T., H. Buist and I. F. Megbolugbe. 1998. An Analysis of the Ex Ante Probabilities of Mortgage Prepayment and Default. Real Estate Economics 26(4): 651-676.zh_TW