Derivatives Topic 5
If LIBOR rates end up being higher than the forward rates, which side of a swap will have positive cash flows?
If LIBOR rates are high, then the floating-rate payer is paying more. Therefore, the fixed-rate payer will have a positive cash flow.
Suppose that you agree to take out a loan and repay it at a rate of LIBOR + 3%. If you wanted to convert it into a fixed-rate loan, which side of an interest rate swap would you take?
You need to be a fixed-rate payer. You would receive a floating rate to pay off the floating interest of your loan, and pay a fixed rate to the counterparty of the swap.
) Explain how you can use a swap to convert a loan denominated in dollars to a loan denominated in euros.
You need to become a euro-payer in a currency swap whose dollar principal and dollar interest rate are equal to those of your loan.
You have a loan with an interest rate of LIBOR + 1.7%. Also, you are a fixed-rate payer in an interest rate swap with an equivalent principal, a fixed rate of 3.8%, and a floating rate equal to LIBOR. What is the effective interest rate of your swap/loan combination?
Your total payment is (LIBOR + 1.7%) + 3.8% - LIBOR = 5.5%.
You decided to speculate on interest rates by becoming a floating-rate payer in a swap. Will you profit if the interest rates are high or low? Explain.
Since you are a floating-rate payer, you pay the floating rate. You profit when this rate is low.
The 2- and 3-year risk-free rates are 3% and 3.7%, respectively, with continuous compounding. What is the value of an FRA according to which you will pay 5% for the third year and receive LIBOR on $1 million. The forward LIBOR rate (annually compounded) for the third year is 5.5%.
The 3-year risk-free rate is 3.7% with continuous compounding. Using the forward LIBOR rate instead of the realized one-year LIBOR rate in the end of year 2, we find that the present value of the cash flow in the end of year 3 is 1,000,000(.055-.05)e^-.037*3=4474.69
Suppose that you are a buyer of an FRA with a quoted rate of 2.3%. If the market interest rate at maturity is 2.4%, will you receive or make a payment?
If you are a buyer of an FRA, then you are paying the fixed rate. Since the quoted fixed rate (2.3%) is lower than the market rate you would face (2.4%), the FRA will result in a payment to you.
A bank finds that its assets are not matched with its liabilities because it is taking floating-rate deposits and making fixed-rate loans. How can swaps be used to offset the risk?
The bank is paying a floating-rate on the deposits and receiving a fixed-rate on the loans. It can offset its risk by entering into interest rate swaps with financial institutions or corporations in which it pays a fixed rate (is a fixed-rate payer) and receives a floating rate.
Suppose that the current risk-free swap rate is LIBOR for 3.5%. If a company wants to convert a bond with a 4% coupon into a loan, what will the effective floating interest rate be?
The company should enter the swap as a floating-rate payer. The total cash outflow will be 4% (to bond holders) + LIBOR - 3.5% = LIBOR + 0.5%. This is the effective floating rate.
The current LIBOR rate for 6-month loans is 1.97%, and the current 3-year LIBOR swap rate is 2.39%. Both rates are semiannually compounded. If you were a floating-rate payer in a swap with a notional principal of $10,000, when would your first payment be? What would be your first total cash flow?
The first exchange of cash flows would be in 6 months. You would receive 2.39%/2 x $10,000 = $119.5 and pay 1.97%/2 x $10,000 = $98.5. Thus, the total cash flow would be $21. It would be positive because you are a floating-rate payer, and the LIBOR (floating) rate is lower than the swap (fixed) rate.
List the most popular types of swaps
The most popular swaps are interest rate swaps, currency swaps, and credit default swaps.
