An evaluation model for interest rate swap which contains prepayment risk

We consider a plain vanilla, fixed-for-floating interest rate swap whose notional principal is equal to the outstanding principal of a loan. Since the outstanding principal of a loan decreases, so does the notional principal of the swap. In some cases the rate of repayment might be higher than the originally expected one, that is, prepayment, in other cases it might be lower than the expected one, that is, arrears. Therefore it may happen that the transition of the amount of outstanding principal differs from the originally expected one. To establish evaluation method of these risks is very important for financial institutions. We deduce an evaluation formula in an analytic form for swap contracts including risks of prepayment and arrears. We also swap rates in analytic form for these swap contracts.