Exam 21: Swaps and Floating Rate Products

Suppose Libor caps and floors at the same strike rate are unequal in price. Suppose that, ceteris paribus, there is a sudden increase in interest-rate volatility. Which of the following statements is valid?

You have sold a $10,000 notional cap consisting of a single caplet with a strike of 6% for a six-month underlying period. All interest rates are computed based on the 30/360 convention. At maturity of the cap period, the underlying interest rate is 7%. What is the net cash flow to you on maturity?

An amortizing interest-rate swap is one in which

You enter into a $100 million notional swap to pay six-month Libor and receive 8%. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the net payment you will receive on September 25 is zero, what must have been the Libor reset on march 25?

You enter into a $100 million notional swap to pay six-month Libor and receive 6%. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the floating rate was reset to 6% on March 25, what is the net amount you will receive on September 25?

The main difference between the "short-form" and "forward" methods of pricing a floating-rate note is:

Consider the following table of prices of five-year semi-annual pay caps and floors: Strike (\%/) Cap price Floor price 4\% 2.50 0.50 5\% 1.50 1.50 6\%/ 0.50 2.50 Assume that the caps and floors also include the first payment in 6 months, so there are 10 payment dates in each instrument. The quoted prices of the caps and floors includes this first payment for which the floating leg has already been set. What is the fixed-rate on a five-year fairly priced swap?

The US and euro-zone day-count convention for a floating-rate note (based on Libor and Euribor, respectively) is

The UK money-market day-count convention is

You have the view that rates will be rising over time. What is thebest kind of swap to exploit this view from among the following alternatives?

Which of the following isnot true of a swaption, i.e., an option on a swap?

Consider a one-year maturity caplet on underlying six-month Libor at a strike rate of 6%. If the forward rate is lognormal with volatility $\sigma = 0.10$ , and the one-year spot rate is 5%, what is the price of a $100,000-notional caplet if the (1,1.5)-year forward rate is 6%?

Consider a one-year caplet on underlying six-month Libor at a strike rate of 6%. If the corresponding floorlet is equal to the caplet in price, what is the current forward rate for the period (1,1.5) years?

The US swap market convention, that is used to compute the fixed payments in a USD swap, is

The 4%-strike six-month Libor-based two-year cap and floor are trading at $2.30 and $2.55, respectively. Assume that the cap has 4 caplets maturing in 6 months, 1 year, 18 months, and 24 months, respectively, and that the floor similarly has 4 floorlets. What is the NPV at inception of a two-year swap in which you are paying Libor versus receiving 4%?

A bank makes long-term fixed-rate loans, and funds itself with short-term deposits. It can best manage its vulnerability to interest rate changes by

Which of the following is not an interest-rate swap?

You enter into a $100 million notional swap to pay six-month Libor and receive 8%. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the floating rate was reset to 6% on March 25, what is the net amount you will receive on September 25?

An equivalent description of the holding of a receive-floating pay-fixed swap is as follows:

If the (1,1.5)-year forward rate is lognormal with volatility $\sigma = 0.15$ , and the one-year spot rate is 4%, what is the NPV of a $100,000-notional $12 \times 18$ -FRA at a 5% strike rate if the (1,1.5)-year forward rate is 6%, as seen from the buyer's point of view? (Assume the Black model applies for interest-rate options.)