Question

The price of a stock is currently $100 per share. The premium on a European put on this share at exercise price $100 (“on the money”) is $5 per share.

a. Suppose an investor purchases this stock and buys a put option for each share she buys. Draw the profit “profile” (profits that would result from every possible stock price outcome by the expiration date of the option). Explain.

b. Compare this pattern with the pattern that results from buying a call option on this stock at the same exercise price. Which is better, the call option or the position in (a)? Explain.

Answer 1

Lets solve this question by taking 2 cases.

Case 1:

• Stock purchase = $100
• Put Option purchase (@100) = $5

Below is the pay off chart for case 1.

Case 2:

• Call Option purchase (@100) = $5

Below is the pay off chart for case 2.

Hence, investing in any of the 2 cases is equivalant. The profit or loss will be same.

But the investment in case 1 is more because of 2 positions involved. Thus, P/L of both the cases will be same whereas ROI of case 2 will be better. If we need to select any 1 case, we should go with case 2.