1. A new financial regulation requires a monthly tax of $0.70 be paid per share on all stock holdings. The payments are due at the end of each month. You are an arbitrageur of single-stock future contracts and are pricing the future contract of a dividend paying stock. The stock currently has a (spot) price of $46.79 and is expected to pay a $1.61 dividend two months from today. The current risk-free rate (in continuously compounded terms) is 3 percent for all maturities. What is the arbitrage-free price of a three-month futures contract? (Enter your answer rounded to the nearest $0.001)
2. The spot price of soybeans is $13.57 per bushel, which costs $0.14 per bushel to store per month (payable at the start of the month). The risk-free rate has a flat term structure with a rate of 4.10 percent per year for all maturities. What is the price for a two-month contract?
3. In one month, a stock will pay a $2.26 dividend. Currently, its spot price is $172.20. The risk-free rate is 5.10 percent for all maturities. What is the three-month arbitrage-free futures price of the stock?
4. A non dividend-paying stock has a spot price of $43.40. The nine month risk-free rate is 5.70 percent per year, continuously compounded. The actual delivery price of the nine-month future contract is $35.18. How much arbitrage profit can we immediately generate from this mispricing?
5. A non-dividend paying stock has a spot price of $29.10. What is the six-month arbitrage-free futures price if the six month risk-free rate is 4.00 percent per year, continuously compounded?