6. Naser is an arbitrage hungry investor, but he did not study well during his derivatives class and needs your help. He observes the price of a European call and put options on Ford is $6. Both options have a strike price of $40 and an expiration date in 3 months. If the risk-free rate is 10% per annum and the stock price of Ford is $38. Investors expect a dividend of $2 after I month. Help Naser identify if there is an arbitrage opportunity and how he can take advantage of it. 5. You want to invest in options. You decided that writing options is a profitable investment. Therefore, you will write 10 naked put option contracts with each contract being on 100 shares. The option price is $30, the time to maturity is 6 months, and the strike price is 192. What is the margin requirement if the stock price is $174? b. How would the answer to (a) change if the rules for index options applied? c. How would the answer to (a) change if the stock price is $210? d. How would the answer to (a) change if you decided buying instead of selling the options? a. 4. A trader has a call option contract to buy 300 shares of a stock for a strike price of $90. What is the effect on the terms of the contract if: a. A $4 dividend being declared b. A $4 dividend being paid c. A 9-for-4 stock split d. A 15% stock dividend being paid. FIN 361 Financial Derivatives Exercise Problems for Chapters 4, 10, 11, 12, 13, and 15 Term Rate 90 days 6.00% 180 days 6.20% 270 days 6.30% 360 days 6.35% 1. Find the rate on a new 6 x 9 FRA. 2. Consider an FRA that was established previously at a rate of 5.2 percent with a notional amount of $30 million. The FRA expires in 180 days, and the underlying is 180-day LIBOR. Find the value of the FRA from the perspective of the party paying fixed and receiving floating as of the point in time at which this term structure applies. 3. STC is planning to implement an aggressive growth strategy in US market. It plans to start a project after 2 years from today, but it is concerned that interest rates will increase when it launches the project and obtains the necessary funding from the debt market. The company plans to pay back the loan 2 years after it receives the loan. STC observes the following zero rates, at which it can both borrow or invest. a. Calculate the 12*24, 24x36, and 36x48 forward rates for the following continuously compounded rates Year Zero Rate 1 3.5% 2 4.0% 4.6% 5.4% b. What is your advice to STC regarding its concern about rising interest rates in the future? What are the necessary steps it needs to take today to lock in the borrowing cost of its project in the future? What will be its borrowing cost? 3 4 6. Naser is an arbitrage hungry investor, but he did not study well during his derivatives class and needs your help. He observes the price of a European call and put options on Ford is $6. Both options have a strike price of $40 and an expiration date in 3 months. If the risk-free rate is 10% per annum and the stock price of Ford is $38. Investors expect a dividend of $2 after I month. Help Naser identify if there is an arbitrage opportunity and how he can take advantage of it. 5. You want to invest in options. You decided that writing options is a profitable investment. Therefore, you will write 10 naked put option contracts with each contract being on 100 shares. The option price is $30, the time to maturity is 6 months, and the strike price is 192. What is the margin requirement if the stock price is $174? b. How would the answer to (a) change if the rules for index options applied? c. How would the answer to (a) change if the stock price is $210? d. How would the answer to (a) change if you decided buying instead of selling the options? a. 4. A trader has a call option contract to buy 300 shares of a stock for a strike price of $90. What is the effect on the terms of the contract if: a. A $4 dividend being declared b. A $4 dividend being paid c. A 9-for-4 stock split d. A 15% stock dividend being paid. FIN 361 Financial Derivatives Exercise Problems for Chapters 4, 10, 11, 12, 13, and 15 Term Rate 90 days 6.00% 180 days 6.20% 270 days 6.30% 360 days 6.35% 1. Find the rate on a new 6 x 9 FRA. 2. Consider an FRA that was established previously at a rate of 5.2 percent with a notional amount of $30 million. The FRA expires in 180 days, and the underlying is 180-day LIBOR. Find the value of the FRA from the perspective of the party paying fixed and receiving floating as of the point in time at which this term structure applies. 3. STC is planning to implement an aggressive growth strategy in US market. It plans to start a project after 2 years from today, but it is concerned that interest rates will increase when it launches the project and obtains the necessary funding from the debt market. The company plans to pay back the loan 2 years after it receives the loan. STC observes the following zero rates, at which it can both borrow or invest. a. Calculate the 12*24, 24x36, and 36x48 forward rates for the following continuously compounded rates Year Zero Rate 1 3.5% 2 4.0% 4.6% 5.4% b. What is your advice to STC regarding its concern about rising interest rates in the future? What are the necessary steps it needs to take today to lock in the borrowing cost of its project in the future? What will be its borrowing cost? 3 4
