Prepayments with Fewer Than 360 Months Remaining
When fewer than 360 months remain in the pool, the applicable PSA prepayment vector is "seasoned" by the pool's age. (Elements in the 360-element prepayment vector that represent past payments are skipped. For example, on a 30-year mortgage that is 10 months old, only the final 350 prepayments are applied.)
Assume, for example, that you have two 30-year loans, one new and another 10 months old. Both have the same PSA speed of 100 and prepay using the vectors plotted below.
Still within the scope of relative valuation, you could also solve for the percentage of the standard PSA prepayment vector given the pool's arbitrary, user-supplied prepayment vector, such that the PSA speed gives the same Macaulay duration as the user-supplied prepayment vector.
If you supply a custom prepayment vector, you must account for the number of months remaining.
Price = 101; Settle = datenum('1-Jan-2001'); Maturity = datenum('1-Jan-2030'); IssueDate = datenum('1-Jan-2000'); GrossRate = 0.08125; PrepayMatrix = 0.005*ones(348,1); CouponRate = 0.075; Delay = 14; ImpliedSpeed = mbsprice2speed(Price, Settle, Maturity, ... IssueDate, GrossRate, PrepayMatrix, CouponRate, Delay)
ImpliedSpeed = 104.2543
Examine the prepayment input. The remaining 29 years require
348 monthly elements in the prepayment vector. Suppose then, keeping
everything the same, you change
Settle to February
Settle = datenum('14-Feb-2003');
You can use
count all incoming coupons received after
NumCouponsRemaining = cpncount(Settle, Maturity, 12, 1, , ... IssueDate)
NumCouponsRemaining = 323
12 defines the monthly payment
1 defines the 30/360 basis, and
aging and determination-of-holder date. Thus, you must supply a 323-element
vector to account for a prepayment corresponding to each monthly payment.
- Fixed-Rate Mortgage Pool
- Prepayment Modeling with a Two Factor Hull White Model and a LIBOR Market Model
- Computing Option-Adjusted Spread
- Pricing Mortgage Backed Securities Using the Black-Derman-Toy Model
- Using Collateralized Mortgage Obligations (CMOs)