多數不動產抵押貸款證券﹝Mortgage Backed Securities﹞的評價方法，乃根據假定的提前清償模型及利率模型，在給予邊界值及終值條件下，找出偏微分方程式的解，但是封閉型解﹝Closed-Form Solution﹞通常不存在，故須利用數值分析方法來求取近似解。在簡化某些條件下，本論文利用半美式可贖回債券﹝Semi- American Callable Bond﹞的模型來評價不動產抵押貸款證券，由於可提前清償時點是有限的，故可找出不動產抵押貸款證券的封閉型解。

由實例研究中得到的結論是：不論利率服從Vasicek或CIR模型，一般付息債券的價格必高於不動產抵押貸款證券；不動產抵押貸款證券的可提前清償的時點數與其價格呈反向關係；隨著期初利率水準的提高，無論可提前清償的時點多寡，選擇權價格皆呈現平滑下降的趨勢。在本研究中亦發現現金流量的分佈與利率模型參數，皆對本不動產抵押貸款證券評價模型造成影響。

一、英文文獻

1.Büttler, Hans-Jürg and Jorg Waldvogel [1996]：“Pricing Callable Bonds by Means of Green's Function,” Mathenatical Finance, 6: pp.53-88.

2.Beaglehole, David R. and Mark S. Tenney [1991]：“General Solutions of Some Interest Rate-Contingent Claim Pricing Equations,” Journal of Fixed Income, pp. 69- 83.

3.Buser, Stephen A., and Patric H. Hendershoot [1984]：“Pricing Default-Free Fixed-Rate Mortgage,” Housing Finance Review, 3: pp.405-429.

4.Cox, John C., Jonathan E. Ingersoll, JR., and Stephen A. Ross [1985a]：“An Intertemporal General Equilibrium Model of Asset Prices,” Econometrica, 53: pp. 363-384.

5.Cox, John C., Jonathan E. Ingersoll, JR., and Stephen A. Ross [1985b]：“A Theory of the Term Structure of Interest Rates,” Econometrica, 53: pp.385-407.

6.Cox, John C., Stephen A. Ross and Mark Rubinstein [1979]：“Option Pricing: A Simplified Approach,” Journal of Financial Economics, 7: pp.229-264.

7.Dunn, K. B., and John J. McConnell [1981]：“Valuation of GNMA Mortgage-Backed Securities,” The Journal of Finance, 36: pp.599-616.

8.Fabozzi, Frank J. [1992]：The handbook of Mortgage Mortgage-Backed Securities, Chicago, Illinois: Probus Publishing.

9.Follain, James F., Louis O. Scott, and T. L. Tyler Yang [1992]：“Microfoundations of a Mortgage Prepayment Function,” Journal of Real Estate Finance and Economics,
5: pp.197-217.

10.Jamshidian, Farshid [1991a]：“Bond and Option Evaluation in the Gaussian Interest Rate Model,” Research in Finance, 9: pp.131-170, JAI Press Inc.

11.Jamshidian, Farshid [1989]：“An Exact Bond Option Formula,” The Journal of Finance, pp.205-209.

12.Jamshidian, Farshid [1987]：“Pricing of Contingent Claims in the One-Factor Term Structure Model,” Working Paper, Merrill Lynch Capital Markets.

13.Kau, J. B., D. C. Keenan, and W. J. Muller Ⅲ [1993]：“An Option-Based Pricing Model of Private Mortgage Insurance,” Journal of Risk and Insurance, pp.288-299.

14.Kau, J. B., D. C. Keenan, W. J. Muller Ⅲ, and J. F. Epperson [1990a]：“Pricing Commercial Mortgages and Their Mortgage-Backed Securities,” Journal of Real Estate Finance and Economics, 3: pp.333-356.

15.Kau, J. B., D. C. Keenan, W. J. Muller Ⅲ, and J. F. Epperson [1987]：“The Valuation and Securitization of Commercial and Multifamily Mortgages,” Journal of Banking and Finance, 11: pp.525-546.

16.Kau, J. B., D. C. Keenan, W. J. Muller Ⅲ, and J. F. Epperson [1985]：“Pricing Default Risk in Mortgages,” American Real Estate and Urban Economics Association, pp.1417-1431.

17.Leung, Wai K. and C. F. Sirmans [1990]： “A Lattice Approach To Fixed-Rate Mortgage Pricing With Default And Prepayment Options,” American Real Estate and Urban Economics Association, 18: pp.91-104.

18.Titman Sheridan and Walter Torous [1989]：“Valuing Commercial Mortgages: An Empirical Investigation of the Contingent-Claims Approach to Pricing Risk Debt,” Journal of Finance, 44: pp.345-373.

19.Vasicek, Oldrich [1977]：“An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, 5: pp.177-188.

20.Y. K. Kwok [1998]：Mathematical Models of Financial Derivatives, Springer.

二、中文文獻

1.周奇勳 [2001]，「美式選擇權之相關研究」，碩士論文，政治大學統計所。

2.陳昆賢 [2001]，「不動產抵押權證券之評價研究--選擇權調整利差法之應用」，碩士論文，朝陽科技大學財務金融所。

3.陳仁遶、廖咸興、楊太樂 [1995]：「抵押貸款訂價模型之效率性—數值分析模型與封閉解模型之比較」，證券市場發展季刊 第七卷第二期 pp.29-45。

4.郭姿伶 [1999]，「住宅貸款之提前清償與逾期還款」，碩士論文，中正大學財務金融所。

5.黃至民 [2001]，「利率可調整之不動產抵押貸款證券之評價與分析」，碩士論文，台灣大學財務金融所。