Suppose that the yield curve is flat at 5%

Suppose that the yield curve is flat at 5% per annum with continuous compounding. A swap with a notional principal of $100 million in which 6% is received and six-month LIBOR is paid will last another 15 months. Payments are exchanged every six months. The six-month LIBOR rate at the last reset date (three months ago) was 7%. Answer in millions of dollars to two decimal places. (i) What is the value of the fixed-rate bond underlying the swap? _ _ _ _ _ _ (ii) What is the value of the floating-rate bond underlying the swap? _ _ _ _ _ _ (iii) What is the value of the payment that will be exchanged in 3 months? _ _ _ _ _ _ (iv) What is the value of the payment that will be exchanged in 9 months? _ _ _ _ _ _ (v) What is the value of the payment that will be exchanged in 15 months? _ _ _ _ _ _ (vi) What is the value of the swap? _ _ _ _ _ _

2. A company can invest funds for five years at LIBOR minus 30 basis points. The fiveyear swap rate is 3%. What fixed rate of interest can the company earn? Ignore day count issues _ _ _ _ _ _ 3

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A stock price is $100. Volatility is estimated to be 20% per year. What is the an estimate of the standard deviation of the change in the stock price in one week?

4. A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use options on the S&P 100 to provide protection against the portfolio falling below$9.5 million. The S&P 100 index is currently standing at 500 and each contract is on 100 times the index. (i) If the portfolio has a beta of 1, how many put option contracts should be purchased? _ _ _ _ _ _ (ii) If the portfolio has a beta of 1, what should the strike price of the put options be? _ _ _ _ _ _ (iii)If the portfolio has a beta of 0.5, how many put options should be purchased? _ _ _ _ _ _ (iv)If the portfolio has a beta of 0.5, what should the strike prices of the put options be? Assume that the risk-free rate is 10% and the dividend yield on both the portfolio and the index is 2%. _ _ _ _ _ _

5. Consider a European put option on a index. The index level is 1,000, the strike price is 1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum. What is a lower bound to the option price? (Give two decimal places.) _ _ _ _ _ _

6. Consider a European call option on a currency. The exchange rate is 1.0000, the strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. What is a lower bound to the option price? (Give four decimal places.) _ _ _ _

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