Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach
Tóm tắt
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.
Tài liệu tham khảo
Downing, C., Stanton, R. and Wallace, N. (2003) An empirical test of a two-factor mortgage valuation model: How much do house prices matter?, Working paper.
Goncharov, Y. (2002) An intensity-based approach for valuation of mortgage contracts subject to prepayment risk, Working paper, University of Illinois.
Jegadeesh, N. and Ju, X. (2000) A non-parametric prepayment model and valuation of mortgage-backed securities. The Journal of Fixed Income 10(1), 50– 67.
Kariya, T. and Kobayashi, M. (2000) Pricing mortgage-backed securities (MBS). Asia-Pacific Financial Markets 7, 189–204.
Kariya, T., Ushiyama, F. and Pliska, S. R. (2002) A 3-factor valuation model for mortgage-backed securities(MBS), Working paper, Kyoto University.
Kau, J. B., Keenan, D. C., Muller, W. J. and Epperson, J. F. (1992) A generalized valuation model for fixed-rate residential mortgages, Journal of Money, Credit, and Banking 24(3), 279–299.
Kau, J. B., Keenan, D. C., Muller, W. J. and Epperson, J. F. (1995) The valuation at origination of fixed-rate mortgage with default and prepayment, Journal of Real Estate Finance and Economics 11, 5–36.
Lando, D. (1998) On cox processes and credit risky securities, Review of Derivatives Research 2, 99–120.
Nakagawa, H. and Shouda, T. (2004) Valuation of mortgage-backed securities based on unobservable prepayment costs, Advances in Mathematical Economics 6, 123–147.
Nakamura, N. (2001) Valuation of mortgage-backed securities based upon a structural approach, Asia-Pacific Financial Markets 8, 259–289.
Schwartz, E. S. and Torous, W. N. (1989) Prepayment and the valuation of mortgage-backed securities, The Journal of Finance 44(2), 375–392.
Schwartz, E. S. and Torous, W. N. (1993) Mortgage prepayment and default decisions: A poisson regression approach, Journal of the American Real Estate and Urban Economics Association 21(4), 431–449.
Shibasaki, T. and Nakamura, N. (2001) Valuation of mortgage-backed securities based upon a hazard rate approach, The 15th JAFEE conference Proceedings (Japanese).
Stanton, R. (1995) Rational prepayment and the valuation of mortgage-backed securities, The Review of Financial Studies 8(3), 667–708.
Sugimura, T. (2002) A prepayment model for the Japanese mortgage loan market: Prepayment-type-specific parametric model approach, Asia-Pacific Financial Markets 9, 305–335.