[Hull, Chapter 28, problem 22, slightly modified.] Calculate the price of a cap on the three-\ month LIBOR rate in nine months' time when the principal amount is

$1000

. Use Black's\ model and the following information:\ The nine-month Eurodollar futures price is 92 (ignore the difference between forwards\ and futures).\ The interest rate volatility implied by a nine-month Eurodollar option is 15 percent per\ annum.\ The current 12-month interest rate with continuous compounding is 7.5 percent per an-\ num.\ The cap rate is 8 percent per annum.\ [Note: by market convention, the Eurodollar futures price refers to a 3-month contract; since\ we are ignoring the difference between forwards and futures, this amounts to a forward term\ rate. So the practical meaning of the first bullet is that we can secure, at no cost now, the\ right to a 3-month Eurodollar contract starting 9 months from now at

100-92=8

percent per\ annum (another market convention).]

[Hull, Chapter 28, problem 22, slightly modified.] Calculate the price of a cap on the threemonth LIBOR rate in nine months' time when the principal amount is $1000. Use Black's model and the following information: - The nine-month Eurodollar futures price is 92 (ignore the difference between forwards and futures). - The interest rate volatility implied by a nine-month Eurodollar option is 15 percent per annum. - The current 12-month interest rate with continuous compounding is 7.5 percent per annum. - The cap rate is 8 percent per annum. [Note: by market convention, the Eurodollar futures price refers to a 3-month contract; since we are ignoring the difference between forwards and futures, this amounts to a forward term rate. So the practical meaning of the first bullet is that we can secure, at no cost now, the right to a 3-month Eurodollar contract starting 9 months from now at 10092=8 percent per annum (another market convention).] [Hull, Chapter 28, problem 22, slightly modified.] Calculate the price of a cap on the threemonth LIBOR rate in nine months' time when the principal amount is $1000. Use Black's model and the following information: - The nine-month Eurodollar futures price is 92 (ignore the difference between forwards and futures). - The interest rate volatility implied by a nine-month Eurodollar option is 15 percent per annum. - The current 12-month interest rate with continuous compounding is 7.5 percent per annum. - The cap rate is 8 percent per annum. [Note: by market convention, the Eurodollar futures price refers to a 3-month contract; since we are ignoring the difference between forwards and futures, this amounts to a forward term rate. So the practical meaning of the first bullet is that we can secure, at no cost now, the right to a 3-month Eurodollar contract starting 9 months from now at 10092=8 percent per annum (another market convention).]