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Answer: -$1.550 million
The financial institution **receives LIBOR** and **pays 3.0% fixed** on a notional of $400 million. ### Cash flow at 0.25 years The floating rate for the next payment was set 0.25 years ago at 3.0%, so the net payment is: \[ \frac{3.0\% - 3.0\%}{2} \times 400 = 0 \] ### Cash flow at 0.75 years The forward LIBOR rate for the period 0.25 to 0.75 is 2.2121% (semi-annual compounding), so the net cash flow is: \[ \frac{2.2121\% - 3.0\%}{2} \times 400 = -1.5758\text{ million} \] ### Discount to present Use the continuously compounded zero rate of 2.20% for 0.75 years: \[ PV = -1.5758 \times e^{-0.022 \times 0.75} \approx -1.550 \text{ million} \] **Correct answer: A**
Author: Manit Arora
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Q-722.2. Suppose that some time ago, a financial institution entered into a swap where it agreed to make semi-annual payments at a rate of 3.0% per annum and receive LIBOR on a notional principal of $400.0 million. The swap now has a remaining life of only nine months (0.75 years). Payments will therefore be made 0.25 and 0.75 years from today. The risk-free rates with continuous compounding is assumed to be the LIBOR zero rate, and currently, it is 2.20% for all maturities. Because the LIBOR zero rate curve is flat at 2.20%, the six-month forward rate beginning in three months, F(0.25, 0.75), is also 2.20% with continuous compounding and therefore is equal to $2 * [\exp(0.0220/2) - 1] = 2.2121%$ with semi-annual compounding. The LIBOR rate applicable to the exchange in 0.25 years was determined 0.25 years ago; suppose it was 3.0% with semi-annual compounding (LIBOR has dropped in the meantime). Note: the question was inspired by Hull's Example 7.1 in his 10th Edition.
Which is nearest to the present value of the swap to the financial institution?
A
-$1.550 million
B
-$287,300
C
+1.883 million
D
+2.940 million
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