Penalty interest payments, though not included in the standard formulas, can affect the price and yield of a mortgage-backed security. PCBOND Manager Software includes the following calculation for the penalty interest cash flow:

PIPk=SRPk · q · r · pipm

where

PIPk=penalty interest cash flow in month k
SRPk=scheduled remaining principal
q=constant monthly liquidation rate
r=weighted average mortgage rate expressed on a monthly basis
pipm=number of month's interest payments charged as a penalty.

Not all mortgage liquidations are subject to penalty. For example, penalties may be waived if the borrower refinances with the same institution. The number of penalty months, pipm, must be adjusted to reflect this. If 50% of liquidations are required to pay a three month penalty, we might use a value of 1.5 for pipm. The term pipm is assumed to be constant for the life of the security.

To incorporate penalties into mortgage-backed security pricing, the penalty interest payment, PIPk, is added to the standard cash flow formula shown in equation [10]:

CFk=(1-c)Bk-1 - Bk + PIPk

Date Published: March 31, 2018