Mathematical theory of mortgage modeling

• Main Author: Goncharov, Yevgeny
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2003
• Subjects: Approximation; Arbitrage; Burnout; Cash flow; Collateral; Collateralized mortgage obligations; Costs; Credit risk; Decision making; Default; Diffusion; Finance; Fixed rates; Interest rates; Liability; Mathematics; Mortgage backed securities; Mortgage rates; Mortgages; Numerical analysis; Prepayments; Probability; Real estate financing; Refinancing; Theory; Valuation
• ISBN: 9780496459308; 0496459309

The models in the literature for valuation of mortgage contracts subject to prepayment can generally be classified into one of two categories: the option-based models and the empirical mortgage-rate-based models. Using risk-neutral martingale methods together with the intensity-based approach borrowed from credit risk modeling, this thesis develops a framework that not only generalizes but considerably extends both approaches and develops new ones. The analysis of prepayment intensity functions and borrower's refinancing incentives advances our understanding of mortgage securities and can make a significant contribution to better prediction of prepayment rates. In particular, we show several reasons why the modern option-based models imply large transaction costs and very slow-to-prepay borrowers. Our general model is not tied to a particular numerical procedure as option-based mortgage models in the literature. As an example we show that classical Stanton's model is in fact just a variant of a splitting-up, numerical method of the first order applied to our model. Throughout the thesis we point out various new ways to develop mortgage modeling.