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CFA Level I Exam · Forward Commitment and Contingent Claim Features and Instruments

Call and Put Option Payoffs and Profit at Expiration

Updated 7 October 2026 · Fact-checked

An option gives the buyer a right, not an obligation, to buy (call) or sell (put) an asset at the exercise price. At expiration a call is worth max(0, S − X) and a put max(0, X − S). Profit equals payoff minus the premium paid. The seller's results are the exact opposite.

Understand Options: Calls, Puts and Payoffs

An option is a contingent claim. The buyer (long) pays a premium to the seller (short, or writer). In return the buyer gets a right. The seller takes on an obligation that applies only if the buyer chooses to exercise.

A call option gives the buyer the right to buy the underlying at the exercise price (strike, X). A put option gives the buyer the right to sell the underlying at X. A call gains when the underlying price rises. A put gains when the price falls.

Moneyness compares the underlying price (S) with the strike. A call is in the money when S > X, at the money when S = X, and out of the money when S < X. A put is the reverse: in the money when S < X, out of the money when S > X. Moneyness tells you whether exercising now would produce a positive value.

Exercise style is about timing. A European option can be exercised only at expiration. An American option can be exercised at any time up to and including expiration. A Bermudan option can be exercised on specified dates. At expiration the payoff formulas are the same for all styles, because on the last day the choice is the same: exercise or not.

The buyer's loss is limited to the premium. A long call has unlimited upside. A long put has a maximum gain of X − premium, since the price cannot fall below zero. The seller's gain is capped at the premium. A short call has unlimited loss. A short put has a maximum loss of X − premium. Option payoffs are zero-sum: the buyer's profit equals the seller's loss.

Key formulas to remember

Long call payoff at expiration
Payoff = max(0, S_T − X)
S_T is the underlying price at expiration. The payoff cannot be negative for the buyer.
Long call profit
Profit = max(0, S_T − X) − c₀
c₀ is the call premium paid. Breakeven price = X + c₀.
Short call payoff and profit
Payoff = −max(0, S_T − X); Profit = c₀ − max(0, S_T − X)
Maximum gain is the premium. Loss is unlimited. Breakeven = X + c₀.
Long put payoff at expiration
Payoff = max(0, X − S_T)
Exercise only if the underlying price is below the strike.
Long put profit
Profit = max(0, X − S_T) − p₀
p₀ is the put premium paid. Breakeven price = X − p₀. Maximum profit = X − p₀.
Short put payoff and profit
Payoff = −max(0, X − S_T); Profit = p₀ − max(0, X − S_T)
Maximum gain is the premium. Maximum loss = X − p₀. Breakeven = X − p₀.
Moneyness
Call ITM if S > X; Put ITM if S < X; ATM if S = X
Out of the money is the opposite of in the money.

How to solve Options: Calls, Puts and Payoffs questions

Use the same routine for any payoff or profit question. Separate payoff from profit, and buyer from seller.

  1. 1Identify the option type (call or put) and your side (long or short).
  2. 2Note S_T, the strike X and the premium. Check whether the question asks for payoff or profit.
  3. 3Decide moneyness at expiration: for a call compare S_T with X; for a put compare X with S_T.
  4. 4Compute the buyer's payoff: max(0, S_T − X) for a call, max(0, X − S_T) for a put.
  5. 5For the buyer, subtract the premium to get profit. For the seller, flip the sign of the buyer's payoff and add the premium.
  6. 6If asked for breakeven or maximum gain or loss, use X + premium for a call, X − premium for a put, and the limits in the concept section.
  7. 7Check the sign and size: the buyer can never lose more than the premium, and buyer and seller figures must sum to zero.

Quickest way: Buyer first, then flip for the seller

When to use it: Use it for any three-option MCQ on payoff, profit or breakeven when you have about 90 seconds.

  1. Work out the long buyer's profit only: intrinsic value minus premium.
  2. If the question is about the seller, change the sign of that answer.
  3. Eliminate any option where the buyer's loss exceeds the premium.
  4. Eliminate any option with a gain above the theoretical maximum, such as a put profit above X − premium.
  5. For breakeven, add the premium to X for a call or subtract it from X for a put.

Common mistakes in Options: Calls, Puts and Payoffs

  • Reporting payoff when the question asks for profit, or the reverse.

    Both terms sound alike and the premium is easy to forget.

    Fix: Underline the word in the question. Profit always includes the premium; payoff never does.

  • Treating a put as in the money when S > X.

    Students carry over the call rule.

    Fix: A put is in the money when the underlying is below the strike. Ask whether selling at X beats selling in the market.

  • Computing a negative payoff for the option buyer.

    Students forget the option is a right and will be left unexercised.

    Fix: The buyer's payoff is max(0, ...). Only the profit can be negative, and it is limited to the premium.

  • Putting the breakeven of a put at X + premium.

    Mixing up call and put breakevens.

    Fix: A put buyer needs the price to fall enough to recover the premium, so breakeven = X − premium.

  • Saying European and American options have different payoffs at expiration.

    Students over-apply the idea that American options are more flexible.

    Fix: The flexibility affects timing before expiration. At expiration both are worth max(0, S − X) for a call and max(0, X − S) for a put.

  • Stating that the writer of a put has unlimited loss.

    Confusion with the short call.

    Fix: The underlying price cannot go below zero, so the short put's maximum loss is X − premium.

Worked examples

Example 1

An investor buys a European call on a share with a strike of $50 for a premium of $3. At expiration the share trades at $58. What is the investor's profit?

Show the solution
  1. Long call, so payoff = max(0, S_T − X).
  2. S_T − X = 58 − 50 = 8, so the call is in the money and payoff = $8.
  3. Profit = payoff − premium = 8 − 3 = $5.
  4. Check: breakeven is 50 + 3 = $53, and 58 is above it, so profit is positive.

Answer: Profit = $5 per share.

Example 2

A trader writes a put with a strike of €40 and receives a premium of €2.50. At expiration the underlying is at €34. What is the trader's profit or loss, and what is the maximum possible loss on the position?

Show the solution
  1. Short put: profit = p₀ − max(0, X − S_T).
  2. X − S_T = 40 − 34 = 6, so the put buyer exercises and the payoff to the writer is −€6.
  3. Profit = 2.50 − 6 = −€3.50, a loss of €3.50.
  4. Maximum loss occurs if the underlying falls to zero: X − p₀ = 40 − 2.50 = €37.50.
  5. Breakeven for the writer is 40 − 2.50 = €37.50, and 34 is below it, which agrees with a loss.

Answer: Loss of €3.50 per share; maximum loss is €37.50 per share.

Exam tips

  • Read whether the question asks for payoff, profit, or value, and whether the position is long or short. Many wrong options are the right number with the wrong sign.
  • Remember that numerical options run from smallest to largest, so a negative profit figure may sit in option A. Check the sign before choosing.
  • Use the maximum gain and loss limits to eliminate options quickly, such as a long put profit above X − premium.
  • Know the profile of each of the four positions: long call, short call, long put, short put. Conceptual questions often ask which position has limited loss or unlimited gain.
  • Do not use the calculator for these items. The arithmetic is simple, so save time for harder questions.

Practice questions from Forward Commitment and Contingent Claim Features and Instruments

Options: Calls, Puts and Payoffs in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Options: Calls, Puts and Payoffs: frequently asked questions

What is the difference between payoff and profit for an option?

Payoff is the value of the option at expiration, max(0, S − X) for a call. Profit is the payoff minus the premium paid for the buyer. For the seller, profit is the premium received minus the amount paid out.

What is the difference between European and American options?

A European option can be exercised only at expiration. An American option can be exercised at any time up to expiration. At expiration the payoff formulas are identical.

How do I find the breakeven price of a call or a put?

For a call, breakeven is the strike plus the premium. For a put, it is the strike minus the premium. At these prices the buyer's and the seller's profit are both zero.

Who has unlimited loss in options?

The writer of a call has unlimited potential loss because the underlying price can rise without limit. The writer of a put has a large but limited loss, equal to the strike minus the premium.