Question

please show work

You purchase one (1) call option with strike price 50 for $ 9 and write three (3) call options with strike 60 for $ 3.

3) What are your anticipations about the stock at maturity (when do you make money)?

Answer 1

Let us first understand the transactions and their significance:

Call option gives the buyer the right to buy the stock at the exercise price for which the buyer pays the seller or the writer an upfront fee called the call premium

Transaction 1: Investor buys 1 call option, with exercise price of 50 and pays a premium of 9

Transaction 2: he writes 3 call options, with exercise price of 60 and receives a premium of 3 each so total premium he received was 9

The premium paid and received cancels each other out and the only reason why the investor entered into transaction 2 was because he anticipated that the options that he has written wont be exercised and the cost incurred by him in purchasing the call option in transaction 1 will be recovered.

So basically he will make money when the price of the stock at the time of expiry of all the options is higher than 50 but lower than 60. If the price is higher than  50, he will exercise his option and buy the stock at 50 and then sell it in the spot market for the spot price which is higher than 50 and the difference will be the profit. This will continue till the spot price is below 60. Once it goes above 60, the investors to whom he has sold the options will exercise their option.

So within the range of 50-60, he will make money.