Valuation models

CMO, ABS and CMBS classes

The collateral pool run monthly at a PSA, CPR or ABS speed with defaults, severity and a recovery lag, then the deal's waterfall (PAC schedule from the band, support, sequential and Z accrual classes, floating classes with caps, losses after overcollateralization from the bottom up), with price and spread, yield, average life, principal window, duration, PV01 and CS01.

Inputs

Classes in order of seniority, one per line: name, balance, coupon, then the kind (sequential, pac, support, z), "float" for a margin over the 1-month rate and "cap 6%"

Class heldFace held (0: the class)Pool balance (0: the classes)Loan coupon (WAC)%Servicing fee%Months left (WAM)Loan age (WALA)monthsAmortization (0: the term)monthsPrepayment modelPrepayment speed% PSAPAC band low% PSAPAC band high% PSADefaults (CDR)%Loss severity%Recovery lagmonthsPrepayment lockoutmonthsPriceDiscount curveDiscount curve: flat rate% cc

Solve the spread from a price

Results

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Methodology

Conventions

The pool runs monthly on one scenario: level payments, prepayments at PSA, CPR or ABS speed, defaults at a CDR with severity and a recovery lag.
Interest pays the classes in order; principal pays the PACs to schedule, then the others in order; a Z accrues while sequential or support classes ahead are outstanding.
Losses come off the overcollateralization, then the classes from the bottom up. The class's flows are discounted on the curve plus a spread solved from a price.

References

Fabozzi, The Handbook of Mortgage-Backed Securities

Formulas

Prepayment: SMM = 1 − (1 − CPR)^(1/12), CPR(PSA) = 6% · min(age, 30)/30 · speed/100
ABS speed: SMMₖ = ABS / (1 − ABS (k − 1))
Value: V = Σ (Iₘ + Pₘ) P(tₘ) e^(−s tₘ)