Tell apart an option's payoff and the profit it earns
The idea
The payoff of a long call at expiry is the greater of zero and the underlying price less the exercise price — it can never be negative, which is the whole point of buying optionality. Profit subtracts the premium paid, so the position loses money for any underlying price below the exercise price plus the premium even where the payoff is positive. For the writer both figures mirror exactly: the writer's maximum profit is the premium and the loss on a naked call is unbounded. Confusing payoff with profit is a common error in reading option diagrams.
Formulas
Profit on a long call
call profit = max(0, Sₜ − X) − premium
- Sₜ
- the price of the underlying at expiry
- X
- the exercise price
- premium
- what was paid for the option at the start
Payoff is what the option pays; profit is what the trade made. The breakeven is X + premium, so an option can finish in the money and still lose money — the commonest confusion in the topic.
A practice question
Can the payoff of a long call option at expiry be negative?
- No — it is the greater of zero and the underlying price less the exercise price — correct
- Yes, if the underlying falls far enoughWhy not: A falling underlying makes the option worthless, which is a payoff of zero rather than a negative one.
- Yes, by the amount of the premiumWhy not: The premium makes the profit negative, not the payoff. The two lines differ by exactly that amount.
The holder simply declines to exercise when the option is out of the money, so the payoff floor is zero. The premium is a separate, already-sunk cost that affects profit, not payoff.
A harder one
A call with an exercise price of 50 cost 4. The underlying finishes at 52. What are the payoff and the profit?
- Payoff 0, profit -4Why not: Treats the option as out of the money. At 52 against a 50 strike it is in the money by 2.
- Payoff 2, profit -2 — correct
- Payoff 2, profit 2Why not: Gets the payoff right and forgets to subtract the 4 paid for it.
The payoff is 52 - 50 = 2, so the option is worth exercising. Subtracting the 4 premium leaves a loss of 2 — exercising still beats letting it expire worthless.
The hardest tier
Why is the maximum loss on a written naked call theoretically unlimited while the maximum loss on a written put is not?
- Because puts are always cash-settledWhy not: Settlement method does not bound a loss, and many puts deliver the underlying.
- Because put writers receive a larger premiumWhy not: Premiums vary with the strike and volatility, and the size of the premium does not cap the loss.
- Because the underlying price has no upper bound but cannot fall below zero — correct
The call writer's loss grows with the underlying without limit. The put writer's worst case is the underlying going to zero, which caps the loss at the exercise price less the premium.
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