Find the fixed rate on a plain vanilla interest rate swap with payments every 180 days (assume a 360-day year)for one year.The prices of Eurodollar zero coupon bonds are 0.9756 (180 days)and 0.9434 (360 days).
A)5.9 percent
B)5 percent
C)6 percent
D)5.5 percent
E)2.95 percent

Question

Quizplus · Accepted Answer

The fixed rate on a plain vanilla interest rate swap can be calculated using the formula for the swap fixed rate, which involves the prices of zero coupon bonds corresponding to the payment periods. The fixed rate is essentially the interest rate that equates the present value of the fixed payments to the present value of the floating payments over the life of the swap. Given the prices of Eurodollar zero coupon bonds for 180 days (0.9756) and 360 days (0.9434), the fixed rate can be calculated as follows:$$ \text{Fixed Rate} = \frac{1 - P(T)}{\sum_{i=1}^{n} P(T_i) \times \Delta T_i} $$Where:- $P(T)$ is the price of the zero coupon bond expiring at the end of the swap, which is 0.9434 for 360 days.- $P(T_i)$ are the prices of the zero coupon bonds for each payment period, which includes 0.9756 for 180 days and 0.9434 for 360 days.- $\Delta T_i$ are the fractions of the year for each payment period, which are 0.5 for 180 days and 0.5 for the next 180 days in a 360-day year.Plugging in the values:$$ \text{Fixed Rate} = \frac{1 - 0.9434}{0.9756 \times 0.5 + 0.9434 \times 0.5} $$$$ \text{Fixed Rate} = \frac{0.0566}{0.9595} $$$$ \text{Fixed Rate} \approx 0.059 \text{ or } 5.9\% $$Therefore, the correct answer is 5.9 percent.

Find the Fixed Rate on a Plain Vanilla Interest Rate