Question

Buying a put option and selling a call option are both considered a way of expressing a bearish view on a stock (i.e., that its price will decline). Draw the hockey-sticks for both buying a put and selling a call in terms of the stock price at expiry S(T), the strike (X), and the premium (C/P). Be sure to label the graphs including breakeven points and upside/downside

Answer 1

Pay off for Buying a put: We have bought the right to sell the stock at price X. We pay the premium p to buy the put option. If the price is less than the strike price then we can buy the stock at a cheaper price from the market and exercise the put option to sell at a profit X-St. Our net profit will be X-St-p (because we paid an amount p to acquire the put option.)

Payoff for selling a call option: We have the obligation to buy the stock at price X. We collected the premium c to sell the call option. This is our instant profit c. If the price is less than the strike price then the call option expires worthless, however if the price is more than strike price then we will have to buy the stock at a costlier price from the market and give it to the option buyer at exercise at a loss of St-X. Our net loss will be St-X-c (because we collected an amount c to sell the call option.)

The graph is copied below:

Put opptn P Call optim