A stock is expected to pay a dividend of $0.75 per share in 1 month, in 4 months, in 7 months, in 10 months, etc. The current stock price is $98.50 and the risk-free rate of interest is 6% per annum with continuous compounding for all maturities. Today you entered into a short position in ten 9-month forward contracts on the stock. (a) What is the forward price, and what is the value of your position (ten short forward contracts) today? (b) Assume that six months later the price of the stock is $100.10 and the risk-free rate is the same as before. What will the forward price be, and what will the value of your position (ten short forward contracts) be? (c) This part is independent of parts (a) and (b). Assume the spot bid/ask quotes for Crude Oil are $48 and $48.6 respectively. Also, assume you can borrow at 5% rate and lend at 1% rate a year (continuously compounded). For what range of one-year forward prices of crude oil there will be NO arbitrage opportunities? Hint: Find a condition on the forward price that would not allow arbitrage opportunities due to overpricing. Then, find another condition on the forward price that would not allow arbitrage opportunities due to underpricing. Then, combine the two conditions and you will find the required range of forward prices. A stock is expected to pay a dividend of $0.75 per share in 1 month, in 4 months, in 7 months, in 10 months, etc. The current stock price is $98.50 and the risk-free rate of interest is 6% per annum with continuous compounding for all maturities. Today you entered into a short position in ten 9-month forward contracts on the stock. (a) What is the forward price, and what is the value of your position (ten short forward contracts) today? (b) Assume that six months later the price of the stock is $100.10 and the risk-free rate is the same as before. What will the forward price be, and what will the value of your position (ten short forward contracts) be? (c) This part is independent of parts (a) and (b). Assume the spot bid/ask quotes for Crude Oil are $48 and $48.6 respectively. Also, assume you can borrow at 5% rate and lend at 1% rate a year (continuously compounded). For what range of one-year forward prices of crude oil there will be NO arbitrage opportunities? Hint: Find a condition on the forward price that would not allow arbitrage opportunities due to overpricing. Then, find another condition on the forward price that would not allow arbitrage opportunities due to underpricing. Then, combine the two conditions and you will find the required range of forward prices
