Explanation:
Assuming 100 PSA:
CPR(month t | t ≤ 30) = 6% × t/30
CPR(month 17) = 6% × 16/30 = 3.2%
150 PSA implies that CPR (at the beginning of month 17) = 1.5 × 3.2% = 4.8%
SMM = 1 − (1 − CPR)^(1/12) = 1 − (1 − 0.048)^(1/12) = 0.409%
Note: The Public Securities Association model prepayment benchmark is one of the models used to estimate the monthly rate of prepayment. It is based on the assumption that rather than remaining constant, the monthly repayment rate gradually increases as a mortgage pool ages. The model assumes that:
(I) CPR = 0.2% for the first month after origination, increasing by 0.2% every month up to 30 months
(II) CPR = 6% for months 30 to 360
Q.3458 Consider a pool of mortgages that were issued exactly 16 months ago at an effective interest rate of 6% p.a (they are beginning the 17th month). What is the CPR, and what is the SMM assuming 150 PSA?
A
CPR = 0.2141%; SMM = 0.01786%
B
CPR = 4.8%; SMM = 0.409%
C
CPR = 5.1%; SMM = 0.4353%
D
CPR = 3.4%; SMM = 0.2878%
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