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?

Answer rating: 100% (QA)

To calculate the price of an atthemoney call option we need to find the expected stock price in the next period Since we do not know the probabilities ... View the full answer