Explanation:
The correct answer is D.
Step 1: Determine the CPR for the 40th month
Since the mortgages are 20-year mortgages, the 40th month falls within the first 12 years (144 months) when the CPR increases at a rate of 0.5% per month.
Under the 100% PSA benchmark, the CPR increases by 0.2% per month in the first 30 months (from 0.2% to 6%). For the 100% PSA benchmark, the CPR ramp-up rate is 0.2% per month (not 0.5%). However, the problem specifies that the CPR is expected to increase at the rate of 0.5% per month.
CPR at the 40th month = 40 × 0.5% = 20% = 0.2
Step 2: Calculate the SMM
Therefore, the SMM for the 40th month is 0.01842.
Q.930 An analyst is analyzing the speed of the prepayments of mortgages in a specific city that are pooled into a mortgage-backed security. Suppose that the Public Securities Association (PSA) prepayment benchmark in the city is 100%, and the monthly conditional prepayment rate (CPR) of 20-year mortgages is expected to increase at the rate of 0.5% from the origination until the end of the 12th year. Then, the CPR is expected to increase at the rate of 0.7% until the maturity of the mortgage. Which of the following is the appropriate estimation of a single monthly mortality rate (SMM) for the 40th month?
A
0.0004
B
0.9313
C
1.248
D
0.01842
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