What is the theoretical/mathematical basis for the valuation of [C]MBS and other structured finance products? Is the methodology mostly consistent across different products?
I can't speak for all structured products but valuing a MBS is straight-forward, but not easy. It's straight-forward because you just need to calculate the net present value of the discounted cash flows. That said, accurately determining those cash flows is hard.
The most difficult cash flows to determine--prepayments and defaults/severity--also have the largest impact on MBS value. Prepayments are highly dependent on interest rates, so an OAS (option-adjusted spread) approach is superior to a static assumption.
The valuation is fairly consistent across different MBS, especially for MBS from the GSEs. A private MBS would likely be more complicated because they don't have the pooling restrictions of the GSEs. CMOs are even more complicated to value because of the tranche structure.
The framework for valuing structured finance products in general is based on the nature of the cashflows in the product.
- Decompose the constituent components of the structure.
- Make some choices about handling the correlations between assets in the structure.
- Review the covenants of the structure and their impact on the cashflows (sequence of events).
Mortgage backed securities are valued by calculating the net present value (NPV) of cash flows they are expected to generate. These cash flows are predicted using a model that incorporates all the contractual characteristics of the security and the underlying loans, as well as assumptions on things like prepayment speed, default speed, loss severity, and forward interest rates. Discount rates are generally determined by adding a spread to the yields on the pricing yield curve. This spread is an observed or assumed market option adjusted spread (OAS) in the case of securities with embedded options or Z-spread in the case of option free bonds.