It is a well known fact that the value of a financial claim reflects the present value of the cash flows produced by the financial claim. While valuing an MBS an important thing to be decided upon is with regard to the cash flows, given the nature of the underlying mortgage contracts.

To an MBS investor, cash flows comprises three components,

CF_t   =   NI_t + SP_t + PR_t

Where,

CF_t   =   total cash flow to investor.

NI_t    =     monthly interest payment net of servicing and other fees.

SP_t   =   scheduled principal payment for month t.

PR_t   =   forecasted unscheduled principal repayments in month t (prepayments).

The significant amount is the prepayment PR_t, which occurs at the discretion of the borrowers.

The following table shows the mechanics of a classical pass through MBS.

Table 

Where,

I_t        =   Gross interest coupon payments

MB_t     =   Mortgage balance

MP_t     =   Monthly scheduled payment of borrowers

SMM_t   =     Standard monthly mortality rate, i.e. prepayment rate, which can also be modelled using more sophisticated econometric techniques

S_t       =     Servicing fee.

Based on the mortgage balance from the previous month, the above process is repeated.

The link between the months follows the dynamic stock adjustment equation

MB_t - MB_t-1 = PR_t + SP_t

Through this equation, the events of one period affect the cash flows of all consequent periods. This is also called path-dependency. Undoubtedly, if it was not for the uncertainty of the prepayments, PR_t, the process would be perfectly predictable on the basis of knowledge of i, s, n, and MB₀.