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except that the swap rate is used instead of the reference rate (3-month LIBOR in our illustration). For example, suppose that the


swap rate is 4.98% and the quarter has 90 days. Then the fixed-rate payment for the quarter is:   $100,000,000 ´ 0.0498 ´ 90 --------- 360 = $1,245,000     If there are 92 days in a quarter, the fixed-rate payment for the quarter is:   $100,000,000´0.0498 ´--9----2--- 360 = $1,272, 667     Note that the rate is fixed for each quarter but the dollar amount of the payment depends on the number of days in the period. SwapsandCaps/Floors     Exhibit 12.3 shows the fixed-rate payments based on different assumed values for the swap rate. The first three columns of the exhibit show the same information as in Exhibit 12.2-the beginning and end of the quarter and the number of days in the quarter. Column (4) simply uses the notation for the period. That is, period 1 means the end of the first quarter, period 2 means the end of the second quarter, and so on. The other columns of the exhibit show the payments for each assumed swap rate.   Calculation of the Swap Rate Now that we know how to calculate the payments for the fixed-rate and floating-rate sides of a swap where the reference rate is 3-month LIBOR given (1) the current value for 3-month LIBOR, (2) the expected 3-month LIBOR from the Eurodollar CD futures contract, and (3) the assumed swap rate, we can demonstrate how to compute the swap rate. At the initiation of an interest rate swap, the counterparties are agree- ing to exchange future payments and no upfront payments are made by either party. This means that the swap terms must be such that the present value of the payments to be made by the counterparties must be at least equal to the present value of the payments that will be received. In fact, to eliminate arbitrage opportunities, the present value of the payments made by a party will be equal to the present value of the payments received by that same party. The equivalence (or no arbitrage) of the present value of the payments is the key principle in calculating the swap rate.