Suppose a stock which pays no dividends sells for 10 today

Problem 5 Suppose a stock, which pays no dividends, sells for \$10 today. Next period, it will either move to \$7 or \$14. You do not know the probabilities of these two outcomes. Riskless zero coupon bonds, paying \$1.10 in one period, cost \$1.00 today.

1. What price would an at-the-money call sell for today?

2. If you wished to synthetically manufacture the at-the-money call option, how many bonds would you buy? How many shares of stock?

3. If the call sold for \$3.00, how would you capture arbitrage profits?

4. Now, consider what the stock might do in the second period. If it moves to \$14 in the first period, it can either move up to \$18 or down to \$11 in the second period. If it moves to \$7 in the first period, it can either move up to \$11 or down to \$4 in the second period. Assuming that riskless zero-coupon bonds, paying \$1.10 in the second period, cost \$1.00 at the end of the first period, what price would an at-the-money call sell for today?