Question

Why would someone need to use a call option? Give a scenario of why someone would want to use one. Also, pick a stock that has a call option written on it and describe how it would benefit someone who would purchase a call option. Showing math is required.

Answer 1

Call option is an option to buy. If a trader decides to exercise his right, then he will buy the shares of a company at the exercise price.

Consider an investor who is bullish (expects that the stock price will go up) about the equity stock of Delia Industries. He buys a 3-month call (takes a long position) on the stock at an exercise price of Rs. 400 by paying a premium of Rs. 40 per share. The profit diagram is as shown above. He will make profit if the stock price goes up. If the stock price remains unchanged or declines, the option expires worthless. Therefore for the stock prices below Rs. 400, the maximum loss is restricted to the option premium of Rs. 40. The breakeven point is equal to the exercise price plus the premium paid, which is Rs. 440 in this case. This shows that the upside potential is unlimited, while the maximum loss is bounded at Rs. 40, which is option premium (i.e. unbounded upside potential and bounded downside risk).

Consider an investor who is moderately bearish (expects that the stock price will go down). He sells a 3-month call (takes a short position, without owning the underlying asset, also called as ‘short call’ or writing a call) on the stock at an exercise price of Rs. 400 by paying a premium of Rs. 40 per share. If the stock price substantially exceeds Rs. 400, the call buyer will exercise the call, which makes a loss to the call writer because he has to buy the stock at price higher than Rs. 400 and sell it at Rs. 400 (we assume that the call writer does not own the stock on which call has been written: a naked call writer).

He will make profit if the stock price goes down. If the stock price remains unchanged at Rs. 400 or declines, the option expires worthless and the call writer makes a profit. Maximum profit is restricted to the option premium of Rs. 40. The breakeven point is equal to the exercise price plus the premium paid. This shows that the upside potential is limited, to Rs. 40, an option premium and potential loss is unlimited (i.e. bounded upside potential and unbounded downside risk).

To minimize the risk, the writer can write an out-of-the-money call. Even though the out-of-the-money call premium is smaller than the premium of an in(at)-the-money call, there is greater probability that he will keep the premium.