Floating-rate payments computation

The quarterly floating-rate payments are based on an actual/360 day count convention. Recall that this convention means that 360 days are assumed in a year and that in computing the interest for the quarter the... 

Now let s return to our objective of determining the future floating-rate payments. These payments can be locked in over the life of the swap using the EURIBOR futures contract. We will show how these floating-rate payments are computed using this contract. 

Exhibit 19.3 shows this for the 3-year swap. Shown in Column (1) is when the quarter begins and in Column (2) when the quarter ends. The payment will be received at the end of the first quarter (March 31 of year 1) and is 1,012,500. That is the known floating-rate payment as explained earlier. It is the only payment that is known. The information used to compute the first payment is in Column (4) which shows the current 3-month EURIBOR (4.05%). The payment is shown in the last column. Column (8). 

We will refer to the present value of 1 to be received in period t as the forward discount factor. In our calculations involving swaps, we will compute the forward discount factor for a period using the forward rates. These are the same forward rates that are used to compute the floating-rate payments—those obtained from the EURIBOR futures contract. We must make just one more adjustment. We must adjust the forward rates used in the formula for the number of days in the period (i.e., the quarter in our illustrations) in the same way that we made this adjustment to obtain the payments. Specifically, the forward rate for a period, which we will refer to as the period forward rate, is computed using the following equation ... 

Given the floating-rate payment for a period and the forward discount factor for the period, the present value of the payment can be computed. For example, from Exhibit 19.3 we see that the floating-rate payment for period 4 is 1,206,222. From Exhibit 19.5, the forward discount factor for period 4 is 0.95689609. Therefore, the present value of the payment is... 

The fixed-rate payer will require that the present value of the fixed-rate payments that must be made based on the swap rate not exceed the 14,052,917 payments to be received from the floating-rate payments. The fixed-rate receiver will require that the present value of the fixed-rate payments to be received is at least as great as the 14,052,917 that must be paid. This means that both parties will require a present value for the fixed-rate payments to be 14,052,917. If that is the case, the present value of the fixed-rate payments is equal to the present value of the floating-rate payments and therefore the value of the swap is zero for both parties at the inception of the swap. The interest rates that should be used to compute the present value of the fixed-rate payments are the same interest rates as those used to discount the floating-rate payments. 

To illustrate this, consider the 3-year swap used to demonstrate how to calculate the swap rate. Suppose that one year later, interest rates change as shown in Columns (4) and (6) in Exhibit 19.8. In Colnmn (4) shows the current 3-month EURIBOR. In Column (5) are the EURIBOR futures price for each period. These rates are used to compute the forward rates in Column (6). Note that the interest rates have increased one year later since the rates in Exhibit 19.8 are greater than those in Exhibit 19.3. As in Exhibit 19.3, the current 3-month EURIBOR and the forward rates are used to compute the floating-rate payments. These payments are shown in Column (8) of Exhibit 19.8. 

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