Question

A 30 year loan's remaining maturity is 340 months, therefore its age is 21 months (360-340+1).  If the PSA is assumed to be 125, what is the corresponding conditional prepayment rate CPR based on the PSA benchmark and a PSA assumption of 125. [Report 4 digits right of decimal i.e. .0001]

Answer 1

When we assume a CPR of x% per annum, it amounts to the assumption of a constant prepayment rate for the life of the mortgage. However, this is contrary to what is observed in reality. Borrowers usually do not sell their homes or refinance their mortgage loan when the loan is fairly new. With the passage of time, the propensity to sell or refinance increases so does the CPR in a linear fashion.

The PSA divided the life of a mortgage loan into two distinct periods. The initial period of 30 months is referred to as ramp.

During this period, the CPR grows linearly at the rate of 0.2% per month, starting from a value of zero, until it attains a value of 6% at the end of the 30th month. After the 30th month, the mortgage is considered to be off the ramp, and the CPR is assumed to remain constant at 6%.

Let n be the number of months after the mortgage was originated. If n<=30, CPR=6*t30%. If t>30, CPR= 6%. This is termed as 100 PSA.

Now CPR at 21st month( time after it was initiated) and PSA assumption of 125

CPR= PSA* number of months after the mortgage was initiated * 0.2( CPR growth in a linear fashion)

CPR= 1.25* 21* 0.2= 5.2500 %

Similarly for months 31-360

CPR= 1.25* 30* 0.2= 7.5000 %