Problem 5 Suppose a stock, which pays no dividends, sells for $10 today. Next pe

Question

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 zerocoupon
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?

Explanation / Answer

1)

1)

It is a situation where an option’s strike price is identical to the price of the underlying security.

Both call and put options will be simultaneously “at the money”.

Thus, the at the money call can be sold at $10/-

Where, no arbitrage occurs.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.