$7\mathrm{.}1.$ Companies A and $B$ have been offered the following rates per annum on a $$20$ million

five$-$year loan:

Company A requires a floating$-$rate loan; Company B requires a fixed$-$rate loan. Design a

swap that will net a bank, acting as intermediary, $0\mathrm{.}1\%$ per annum and that will appear

equally attractive to both companies.

$7\mathrm{.}2.$ A $$100$ million interest rate swap has a remaining life of $10$ months. Under the terms of the

swap, six$-$month LIBOR is exchanged for $4\%$ per annum $($compounded semiannually$).$ Six$-$

month LIBOR forward rates for all maturities are $3\%($with semiannual compounding$).$

The six$-$month LIBOR rate was $2\mathrm{.}4\%$ two months ago. OIS rates for all maturities are

$2\mathrm{.}7\%$ with continuous compounding. What is the current value of the swap to the party

paying floating? What is the value to the party paying fixed?

$7\mathrm{.}3.$ Company $x$ wishes to borrow U$.$S$.$ dollars at a fixed rate of interest. Company $Y$ wishes

to borrow Japanese yen at a fixed rate of interest. The amounts required by the two

companies are roughly the same at the current exchange rate. The companies have been

quoted the following interest rates, which have been adjusted for the impact of taxes:

Design a swap that will net a bank, acting as intermediary, $50$ basis points per annum.

Make the swap equally attractive to the two companies and ensure that all foreign

exchange risk is assumed by the bank.

$7\mathrm{.}4.$ A currency swap has a remaining life of $15$ months. It involves exchanging interest at

$10\%$ on $20$ million for interest at $6\%$ on $$30$ million once a year. The term structure of

risk$-$free interest rates in the United Kingdom is flat at $7\%$ and the term structure of risk$-$

free interest rates in the United States is flat at $4\%($both with annual compounding$).$ The

current exchange rate $($dollars per pound sterling$)$ is $1\mathrm{.}5500.$ What is the value of the

swap to the party paying sterling? What is the value of the swap to the party paying

dollars?

$7\mathrm{.}5.$ Explain the difference between the credit risk and the market risk in a swap.

$7\mathrm{.}6.$ A corporate treasurer tells you that he has just negotiated a five$-$year loan at a competitive

fixed rate of interest of $5\mathrm{.}2\%.$ The treasurer explains that he achieved the $5\mathrm{.}2\%$ rate by

borrowing at a six$-$month floating reference rate plus $150$ basis points and swapping the

floating reference rate for $3\mathrm{.}7\%.$ He goes on to say that this was possible because his

company has a comparative advantage in the floating$-$rate market. What has the trea$-$

surer overlooked? Companies A and B have been offered the following rates per annum on a $$20$ million $5$ year loan: $\backslash$table$[[,$Fixed Rate,Floating Rate$],[$Company A$,5\mathrm{.}0\%,$SOFR $+0\mathrm{.}1\%$