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Collateral Risk in Residential Mortgage Defaults

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Abstract

This paper presents a systematic framework for capturing the collateral-driven mortgage default risk. A forward-looking home price distribution model is developed that explicitly incorporates different sources of volatility in the market value of collateral houses. A consistent and computationally-efficient top-down approach of home price simulation is also introduced. We show that with the proper inclusion of all relevant sources of volatilities, the top-down approach provides close approximation to the results generated by a theoretically sound but computationally demanding bottom-up simulation approach. Using a numerical simulation, we demonstrate that a geographically-diversified mortgage pool entails a substantially lower level of systematic collateral driven mortgage default risk compared to a spatially-concentrated pool. However, the expected default risk is shown to remain unaffected, indicating that the benefit from geographic diversification is only realized through lower risk-based capital requirements, not in lower mortgage insurance premiums. Based on the US state level house price indices, the systematic risk of a state-concentrated mortgage pool is estimated to be about four times higher than that of a nationally-diversified mortgage pool. Our results also show that, among the different volatility components, omitting the cross-sectional dispersion of individual home prices would produce the largest bias in assessing home-price-based mortgage default risk.

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Notes

  1. See Vandell (1993), Kau et al. (1994), Yang et al. (1998), Deng et al. (2000), and Calhoun and Deng (2002). Some early option-based mortgage default models include Foster and Van Order (1984), Epperson et al (1985), and Vandell and Thibodeau (1985).

  2. Merrill Lynch (2006) essentially used alternative home price scenarios to perform a sensitivity analysis in their subprime loss projections, while Lehman Brothers (2006) attempt to derive an implied distribution of home price appreciations (HPA). The benchmark HPA distributions employed by the two institutions are widely variant.

  3. See Deng et al. (2000), Ambrose et al. (2005), Calhoun and Deng (2002), and IFE Group (2007) for details.

  4. Remember that the theoretical methodology developed herein can be applied to any geographical area as long as the area HPI is observed. The assumption we made here is valid because public state-level HPI forecast is not available and also not many institutions have internal research capacity to consistently conduct forecasts of the 50 individual states. Later in our numerical example the OFHEO state-level historical HPI and also their dispersion parameters a and b are used to estimate the HPA due to its accessibility. With the limitation of unobserved forward state-level HPI, to forecast the future change in housing values, a market available national HPA forecast can be leveraged and in so doing an additional layer of uncertainty regarding the dispersion of state-level HPA against the national-level HPA is required.

  5. The FHA Actuarial Review (2007) estimated the parameter c to be 0.0007394 and 0.0007663 among the 9 Census regions and among the 43 largest MSAs, respectively, using data up to 2005Q2.

  6. In their model, default estimates were based on a multinomial logit model for quarterly conditional probability of default terminations. Our numerical analysis measures effects of the different volatility components on ex-ante distribution of the probability of negative equity (Pneq) and probability of default (PD) of a pool of homogenous mortgages. The parameters of a representative mortgage required in applying Calhoun and Deng (2002) conditional default rate model include 90% original LTV,1.1 mortgage premium value, 1.1 slope of the yield curve, 1.2 relative loan size ratio, current season being “fall,” burnout (dummy) being 0, 30 year maturity, owner-occupied property, current loan age and also age square, and the current Pneq estimated from our model.

  7. See Calhoun and Deng (2002), and IFE Group (2007).

  8. The risk involved in a deterministic future state/national HPA case is similar to that of a historical realized state/national HPA. There exists only dispersion but no forecasting error.

  9. Our results confirm the prior finding by Calem and LaCour-Little (2004) in that geographical diversification can reduce the capital holding.

References

  • Abraham, J. M., & Schauman, W. S. (1991). New evidence on home prices from Freddie Mac repeat sales. AREUEA Journal, 19(3), 2333–2352.

    Google Scholar 

  • Ambrose, B., LaCour-Little, M., & Huszar, Z. (2005). A note on hybrid mortgages. Real Estate Economics, 33(4), 765-782.

    Article  Google Scholar 

  • Calem, P., & LaCour-Little, M. (2004). Risk-based capital requirements for mortgage loans. Journal of Banking and Finance, 28, 647–672.

    Article  Google Scholar 

  • Calhoun, C. A. (1996). OFHEO house price indexes: Technical description. D.C., Office of Federal Housing Enterprise Oversight: Washington. April.

    Google Scholar 

  • Calhoun, C. A., & Deng, Y. (2002). A dynamic analysis of fixed- and adjustable-rate mortgage terminations. Journal of Real Estate Finance and Economics, 24(1/2), 9–33.

    Article  Google Scholar 

  • Case, K. E., & Schiller, R. J. (1987). Prices of single family homes since 1970: new indexes for four cities. New England Economic Review, 45–56.

  • Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–407.

    Article  Google Scholar 

  • Deng, Y., Quigley, J. M., & Van Order, R. (2000). Mortgage termination, heterogeneity, and the exercise of mortgage options. Econometrica, 68(2), 275–307.

    Article  Google Scholar 

  • Epperson, J. F., Kau, J. B., Keenan, D. C., & Muller, W. J. I. I. I. (1985). Pricing default risk in mortgages. AREUEA Journal, 13(3), 261–272.

    Google Scholar 

  • Foster, C., & Van Order, R. (1984). An options-based model of mortgage default. Housing Finance Review, 3(4), 351–372.

    Google Scholar 

  • Gorton, G. (2008). The Pnic of 2007. Presented at the 2008 Kansas City Fed Annual Meeting, Jackson Hole, Wyoming.

  • 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(1), 77–105.

    Article  Google Scholar 

  • IFE Group. (2007). An Actuarial Review of the Federal Housing Administration Mutual Mortgage Insurance Fund for Fiscal Year 2007. Report to the U.S. Department of Housing and Urban Development.

  • Kau, J. B., Keenan, D. C., & Kim, T. (1994). Default probabilities for mortgages. Journal of Urban Economics, 35, 278–296.

    Article  Google Scholar 

  • Lehman Brothers (2006). Introduing Credit OAS for Residential Mortgage Securities. Fixed Income Research.

  • Longstaff, F. A., & Schwartz, E. S. (1992). Interest rate volatility and the term structure: a two-factor general equilibrium model. Journal of Finance, 47(4), 1259–1282.

    Article  Google Scholar 

  • Merrill Lynch (2006). Valuing Subordinate ABS. Global Securities Research.

  • Vandell, K. (1993). Handing over the keys: a perspective on mortgage default research. Real Estate Economics, 21(3), 211–246.

    Article  Google Scholar 

  • Vandell, K., & Thibodeau, T. (1985). Estimation of mortgage defaults using disaggregate loan history data. AREUEA Journal, 13(3), 929–1316.

    Google Scholar 

  • Vasicek, O. A. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.

    Article  Google Scholar 

  • Yang, T. T., Buist, H., & Megbolugbe, I. F. (1998). An analysis of ex-ante probability of mortgage prepayment and default. Real Estate Economics, 26(4), 651–676.

    Article  Google Scholar 

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Authors and Affiliations

  1. IFE Group, 51 Monroe Street, Suite 801, Rockville, MD, 20850, USA

    Tyler T. Yang

  2. National Tsing Hua University, 101, Sec. 2, Kuang-Fu Road, Hsin-Chu, 30013, Taiwan, Republic of China

    Che-Chun Lin

  3. The KDI School of Public Policy and Management, P.O.Box 184, Cheong-Nyang, Seoul, 130-868, Korea

    Man Cho

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  1. Tyler T. Yang
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  2. Che-Chun Lin
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  3. Man Cho
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Correspondence to Tyler T. Yang.

Additional information

The research supports from the National Science Council of Taiwan (NSC96-2415-H-007-011-MY2 for C. C. Lin) are gratefully acknowledged.

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Yang, T.T., Lin, CC. & Cho, M. Collateral Risk in Residential Mortgage Defaults. J Real Estate Finan Econ 42, 115–142 (2011). https://doi.org/10.1007/s11146-009-9194-y

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