Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach
- 129 Downloads
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.
Keywordscompeting risks default risk intensity-based approach mortgage valuation prepayment risk RMBS
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- Goncharov, Y. (2002) An intensity-based approach for valuation of mortgage contracts subject to prepayment risk, Working paper, University of Illinois.Google Scholar
- 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.Google Scholar
- Kariya, T., Ushiyama, F. and Pliska, S. R. (2002) A 3-factor valuation model for mortgage-backed securities(MBS), Working paper, Kyoto University.Google Scholar
- Lando, D. (1998) On cox processes and credit risky securities, Review of Derivatives Research 2, 99–120.Google Scholar
- Nakagawa, H. and Shouda, T. (2004) Valuation of mortgage-backed securities based on unobservable prepayment costs, Advances in Mathematical Economics 6, 123–147.Google Scholar
- Shibasaki, T. and Nakamura, N. (2001) Valuation of mortgage-backed securities based upon a hazard rate approach, The 15th JAFEE conference Proceedings (Japanese).Google Scholar