Analyzing yield, duration and convexity of mortgage loans under prepayment and default risks
In this article, we construct a general model, which considers the borrower's financial and non-financial termination behavior, to derive the closed-form formula of the mortgage value for analyzing the yield, duration and convexity of the risky mortgage. Since the risks of prepayment and default are reasonably expounded in our model, our formulae are more appropriate than traditional mortgage formulae. We also analyze the effects of the prepayment penalty and partial prepayment on the yield, duration and convexity of a mortgage, and provide lenders with an upper-bound for the mortgage default insurance rate. Our model provides portfolio managers a useful framework to more appropriately appraise the mortgage and more effectively hedge their mortgage holdings. From the results of sensitivity analyses, we find that higher interest-rate, prepayment and default risks will increase the mortgage yield and reduce the duration and convexity of the mortgage.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- John M. Quigley & Robert Order, 1990. "Efficiency in the Mortgage Market: The Borrower's Perspective," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 18(3), pages 237-252.
- Haensly, Paul J & Springer, Thomas M & Waller, Neil G, 1993. "Duration and the Price Behavior of Fixed-Rate Level Payment Mortgages: An Analytical Investigation," The Journal of Real Estate Finance and Economics, Springer, vol. 6(2), pages 157-66, March.
- Azevedo-Pereira, Jose A & Newton, David P & Paxson, Dean A, 2003. "Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation," The Journal of Real Estate Finance and Economics, Springer, vol. 26(2-3), pages 197-221, March-May.
- Brent W. Ambrose & Charles A. Capone, 1998. "Modeling the Conditional Probability of Foreclosure in the Context of Single-Family Mortgage Default Resolutions," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 26(3), pages 391-429.
- Brent W. Ambrose & Richard J. Buttimer Jr., 1998.
"Embedded Options in the Mortgage Contract,"
Zell/Lurie Center Working Papers
305, Wharton School Samuel Zell and Robert Lurie Real Estate Center, University of Pennsylvania.
- Eduardo S. Schwartz & Walter N. Torous, 1993. "Mortgage Prepayment and Default Decisions: A Poisson Regression Approach," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(4), pages 431-449.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(3), pages 599-616, June.
- Lambrecht, Bart M & Perraudin, William R M & Satchell, Steven, 2003. " Mortgage Default and Possession under Recourse: A Competing Hazards Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(3), pages 425-42, June.
- Esa Jokivuolle & Samu Peura, 2003. "Incorporating Collateral Value Uncertainty in Loss Given Default Estimates and Loan-to-value Ratios," European Financial Management, European Financial Management Association, vol. 9(3), pages 299-314.
- Ambrose, Brent W & Sanders, Anthony B, 2003. "Commercial Mortgage-Backed Securities: Prepayment and Default," The Journal of Real Estate Finance and Economics, Springer, vol. 26(2-3), pages 179-96, March-May.
- Tyler T. Yang & Henry Buist & Isaac F. Megbolugbe, 1998. "An Analysis of the "Ex Ante" Probabilities of Mortgage Prepayment and Default," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 26(4), pages 651-676.
- Childs, Paul D & Ott, Steven H & Riddiough, Timothy J, 1997. "Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums," The Journal of Real Estate Finance and Economics, Springer, vol. 14(3), pages 263-82, May.
- Merton, Robert C, 1974.
"On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,"
Journal of Finance,
American Finance Association, vol. 29(2), pages 449-70, May.
- Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Kau, James B, et al, 1993. "Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages," The Journal of Business, University of Chicago Press, vol. 66(4), pages 595-618, October.
- Timothy J. Riddiough & Howard E. Thompson, 1993. "Commercial Mortgage Pricing with Unobservable Borrower Default Costs," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(3), pages 265-291.
- Deng, Yongheng & Quigley, John M. & Van Order, Robert & Mac, Freddie, 1996.
"Mortgage default and low downpayment loans: The costs of public subsidy,"
Regional Science and Urban Economics,
Elsevier, vol. 26(3-4), pages 263-285, June.
- Yongheng Deng & John M. Quigley & Robert Van Order, 1995. "Mortgage Default and Low Downpayment Loans: The Costs of Public Subsidy," NBER Working Papers 5184, National Bureau of Economic Research, Inc.
- Fang-xiong Gong & Joseph Gyourko, 1998. "Evaluating the Costs of Increased Lending in Low and Negative Growth Local Housing Markets," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 26(2), pages 207-234.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Gady Jacoby, 2003. "A Duration Model For Defaultable Bonds," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 26(1), pages 129-146.
- Berger, Allen N. & Udell, Gregory F., 1990.
"Collateral, loan quality and bank risk,"
Journal of Monetary Economics,
Elsevier, vol. 25(1), pages 21-42, January.
- Kelly, Austin & Slawson, V Carlos, Jr, 2001. "Time-Varying Mortgage Prepayment Penalties," The Journal of Real Estate Finance and Economics, Springer, vol. 23(2), pages 235-54, September.
- Chance, Don M, 1990. " Default Risk and the Duration of Zero Coupon Bonds," Journal of Finance, American Finance Association, vol. 45(1), pages 265-74, March.
- Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
- James B. Kau & Donald C. Keenan & Taewon Kim, 1993. "Transaction Costs, Suboptimal Termination and Default Probabilities," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(3), pages 247-263.
- Chiang, Raymond C & Chow, Ying-Foon & Liu, Ming, 2002. "Residential Mortgage Lending and Borrower Risk: The Relationship between Mortgage Spreads and Individual Characteristics," The Journal of Real Estate Finance and Economics, Springer, vol. 25(1), pages 5-32, July.
- Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
- Collin-Dufresne, P & Harding, John P, 1999. "A Closed Form Formula for Valuing Mortgages," The Journal of Real Estate Finance and Economics, Springer, vol. 19(2), pages 133-46, September.
When requesting a correction, please mention this item's handle: RePEc:eee:jhouse:v:18:y:2009:i:2:p:92-103. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.