1. A corporation enters into a $35 million notional principal plain vanilla interest rate swap. The swap calls for the corporation to pay a fixed rate and receive a floating rate of LIBOR. The payments will be made every three months for one year. The term structure of LIBOR when the swap is initiated is as follows:
|
Months
|
Rate (%)
|
|
3
|
7.00
|
|
6
|
7.25
|
|
9
|
7.45
|
|
12
|
7.55
|
Assume all of rates are continuously compounded.
a. Determine the fixed rate on the swap.
b. Calculate the first net payment on the swap.
2. PQR Company longs a FRA on 2-month LIBOR with a fixed rate of 5.25 percent and a notional principal of $38 million. If the market LIBOR rate is 6.125 percent at expiration, what would be the payoff of this FRA to PQR? Assume that there are 30 days in a month.
3. A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 10% and annual volatility of 25%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 20% and an annual volatility of 20% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these tow stocks is 0.2.
a. Compute the 5% annual VAR for the portfolio.
b. If the firm sells $10 million of stock A and buys $10 million of stock B, by how much does the 5% annual VAR change?
4. Given interest rate options with notional principals of $10 million on an underlying 120-day LIBOR. The options have exercise rates of 6% and will expire in 30 days.
a. What is the payoff on the call option if the LIBOR in 30 days is 7%, in 60 days is 8%, and in 90 days is 9%?
b. What is the payoff on the put option if the LIBOR in 30 days is 3%, in 60 days is 4%, and in 90 days is 5%?
c. Discuss the difference between the payoff on an FRA and the payoff on an interest rate option.