Question

The current price of the Gilead stock is $77 per share. Consider an option strategy, which consists of following positions: (1) Selling one put option on the Gilead stock with the strike price of $75. The price of this put option is $3.44. (2) Buying one put option on the Gilead stock with the strike price of $72. The price of this option is $2.24. (3) Buying one call option on the Gilead stock with the strike price of $81. The price of this option is $3.10. (4) Selling one call option on the Gilead stock with the strike price of $79. The price of this option is $3.90 All options expire in 3 months.

1. Construct the payoff table for this strategy at expiration;

2. Construct the graph, which illustrates the payoff of this strategy at expiration. The payoff table should help you to construct this graph.

3. What is the cost of this strategy?

4. Draw the graph, showing profit/loss of this strategy at expiration (you can disregard the time value of money); 5. In your opinion, what is the rationale for constructing this strategy?

Answer 1

Payoff of a long call option = Max[S-X, 0] - P

Payoff of a short call option = P - Max[0, S-X]

Payoff of a long put option = Max[X-S, 0] - P

Payoff of a short put option = P - Max[0, X-S]

S = underlying price at expiry,

X = strike price

P = premium paid or received (long options involve paying premium, and short options receive premium)

Cost of this strategy = net premium received = $3.44 + $3.90 - $2.24 - $3.10 = $2.00

The rationale for constructing this strategy is that the investor expects the stock price to stay within a certain range, between $73 and $81. This would result in a profit for the investor. However, if the stock price goes beyond these levels, the losses are limited.