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Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

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  • Toru Sugimura

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Abstract

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported. Copyright Springer Science+Business Media, Inc. 2004

Suggested Citation

  • Toru Sugimura, 2004. "Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(2), pages 185-214, June.
    • Handle: RePEc:kap:apfinm:v:11:y:2004:i:2:p:185-214
    DOI: 10.1007/s10690-006-9009-6
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    References listed on IDEAS

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    1. Downing, Chris & Stanton, Richard & Wallace, Nancy E., 2003. "An Empirical Test of a Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?," Research Program in Finance, Working Paper Series qt2qb613r5, Research Program in Finance, Institute for Business and Economic Research, UC Berkeley.
    2. 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.
    3. Chris Downing & Richard Stanton & Nancy Wallace, 2003. "An empirical test of a two-factor mortgage valuation model: how much do house prices matter?," Finance and Economics Discussion Series 2003-42, Board of Governors of the Federal Reserve System (US).
    4. Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-299, August.
    5. Kau, James B. & Keenan, Donald C. & Muller III, Walter J. & Epperson, James F., 1995. "The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment," The Journal of Real Estate Finance and Economics, Springer, vol. 11(1), pages 5-36, July.
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