Question

An investor buys a European call on a share for $5. The current stock price is $102 and the strike price is $100. (a) Under what circumstances will the investor make a profit (have positive profit) on the expiration date? (b) Under what circumstances will the option be exercised on the expiration date? (c) Please draw a diagram showing how the investor’s profit depends on the stock price on the expiration date. To put it another, draw a diagram showing the relationship between the investor’s profit and the stock price on the expiration date

Answer 1

European call option gives the option buyer an option to buy the specified share from the option seller at a predetermined price at the date of expiry of the share. The predetermined price is known as the strike price. The option buyer has to pay the option seller an amount for the option. This is known as option premium.

a) In this case, the strike price is $100 and premium is $5.

On the date of expiry, there are 3 possibilities:

1. Market price is below $100. In such a case, there is no point in exercising the option and buying the share for $100 when you can buy it from the market at a lower price. The option premium paid to the option seller is not recoverable. So it is considered a loss.

2. Market price is $100. In such a case, the option may or may not be exercised. The strike price and market price are the same. Even if you exercise the option and buy the share at $100, you will not earn any profits by selling it at the market because you will only get $100 for it. Again, the option premium is a loss.

3. Market price is above $100. In such a case, the option buyer will exercise the option and buy the shares from the option seller at $100. He will then sell these shares at the market at a higher rate and earn profit. Since the option premium is a loss, he will need to earn a higher profit than the option premium so that net profit is positive. However, it will be more profitable than not exercising the option at all.

Therefore, The investor will have a positive profit on expiration date if the market price is more than $105

Let us assume market price is $106.

Profit on share = 106-100 = 6

Less: share premium = 5

Net profit = 6 - 5 = $1

b) As explained earlier,

when market price is $100, the investor may or may not exercise the option.

When the market price is above $100, the investor will definitely exercise the option.

c) diagram showing how the investor’s profit depends on the stock price on the expiration date

Hope that covers your question. If there's anything else you need me to add to the answer, please let me know in the comments below. :)