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 changeSettleto February 14, 2003.

Settle = datenum('14-Feb-2003');

You can usecpncountto count all incoming coupons received afterSettleby invoking

NumCouponsRemaining = cpncount(Settle, Maturity, 12, 1, [],...IssueDate)

NumCouponsRemaining = 323

The input12defines the monthly payment frequency,1defines the 30/360 basis, andIssueDatedefines aging and determination-of-holder date. Thus, you must supply a 323-element vector to account for a prepayment corresponding to each monthly payment.

See Also

mbscfamounts|mbsconvp|mbsconvy|mbsdurp|mbsdury|mbsnoprepay|mbspassthrough|mbsprice|mbswal|mbsyield|mbsprice2speed|mbsyield2speed|psaspeed2default|psaspeed2rate|mbsoas2price|mbsoas2yield|mbsprice2oas|mbsyield2oas

Related Examples

• 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)

More About

• What Are Mortgage-Backed Securities?