Payoff and profit of a call option
1. The idea
A call option gives its buyer the right to buy a share at a fixed price, the strike price, on the expiry date. The buyer pays for that right when buying the option: the premium. At expiry the buyer exercises only if the share is worth more than the strike price, and then gains the difference. That gain is the payoff. The profit also subtracts the premium:
\[ \begin{aligned} \text{payoff} &= \max(S_T - K,\ 0),\\ \text{profit} &= \max(S_T - K,\ 0) - c, \end{aligned} \]
where \(S_T\) is the share price at expiry, \(K\) the strike price and \(c\) the premium paid for the call. The profit is $0 at the break-even share price, \(S_T = K + c\).
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
3. Payoff and profit on one chart
In the question, the strike price is $100 and we paid an $8 premium. The share ends at $120, so we use our right and buy at $100 a share worth $120. The payoff is $20, and after the $8 premium our profit is $20 − $8 = $12.
Now move the share price at expiry and watch both lines. The profit line is the payoff line moved down by the $8 premium.
The chart has three cases:
- At or below the $100 strike price. We do not exercise. The payoff is $0, and we lose the $8 premium.
- Between $100 and the $108 break-even. We exercise, but the payoff is less than the $8 premium, so we still lose money. This is the case most often missed.
- At or above $108. The payoff covers the premium, so our profit is $0 or more.
4. One worked example, then your turn
The worked example is in the middle case: the option is exercised and still loses money.
Now the same steps with hints, one step at a time.
And one on your own.
5. Practice
Each question has new numbers. You master the skill when you get three right in a row, with at least one right answer in each of the three cases. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day. Practice spread over several days keeps a skill far longer than the same amount of practice on one day.
This skill: