Mortgage-backed securities (MBS) are among the most complex of all financial instruments. Analysis of MBS requires blending empirical analysis of borrower behavior with the mathematical modeling of interest rates and home prices. Over the past 25 years, Andrew Davidson and Alexander Levin have been at the leading edge of MBS valuation and risk analysis. Mortgage Valuation Models: Embedded Options, Risk, and Uncertainty contains a detailed description of the sophisticated theories and advanced methods that the authors employ in real-world analyses of mortgage-backed securities. Issues such as complexity, borrower options, uncertainty, and model risk play a central role in the authors' approach to the valuation of MBS. The coverage spans the range of mortgage products from loans and TBA (to-be-announced) pass-through securities to subordinate tranches of subprime-mortgage securitizations. With reference to the classical CAPM and APT, the book advocates extending the concept of risk-neutrality to modeling home prices and borrower options, well beyond interest rates. It describes valuation methods for both agency and non-agency MBS including pricing new loans; approaches to prudent risk measurement, ranking, and decomposition; and methods for modeling prepayments and defaults of borrowers. The authors also reveal quantitative causes of the 2007-09 financial crisis and provide insight into the future of the U.S. housing finance system and mortgage modeling as this field continues to evolve. This book will serve as a foundation for the future development of models for mortgage-backed securities.

Mortgage Valuation Models: Embedded Options, Risk, and Uncertainty (Financial Management Association Survey and Synthesis)

Business & Money

Davidson, Andrew

Levin, Alexander

Economics

Oxford University Press

Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrown the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a mathematical maturity of an advanced undergraduate.

Difference Algebra (Algebra and Applications, 8)

Science & Math

Mathematics

Springer

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Books by Levin, Alexander