Andrew Kalotay, Deane Yang
Prepayment modeling is the dominant consideration of MBS valuation. Projections of future prepayments are typically derived from historical data. Periods of rampant refinancings, such as the fall of 2001, inevitably give rise to "new and improved" prepayment models. "Burnout" (the slow-down following major refinancing activity) is usually modeled by changing parameters.
We introduce a new CLEAN* approach to valuing mortgage-backed securities. "Baseline" prepayments that do not depend on interest rates are modeled using a vector of prepayment speeds, while refinancings are modeled using an option-based approach. The full spectrum of refinancing behavior is described using the notion of refinancing efficiency. There are financial engineers who refinance at just the right time, leapers who do it too early, and laggards who wait too long.
The initial mortgage pool is partitioned into "efficiency buckets", whose sizes are calibrated to market prices. The composition of the seasoned pool is then determined by the amount of excess refinancings over baseline prepayments. Leapers are eliminated first, then financial engineers, and finally laggards. As the pool ages, its composition gradually shifts towards laggards, and this automatically accounts for burnout.
A distinguishing feature of our approach is the rigorous analysis of mortgages. It requires an optionless mortgage yield curve that is not explicitly observable but is implied by market data. Mortgage rates and MBS rates are represented as two perfectly correlated lattices: one determines mortgage refinancings; the other values the MBS. This formulation allows for recursive valuation that is orders of magnitude faster than conventional Monte Carlo analysis, resulting in increased accuracy and superior performance.