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Common Payoff Shapes

Eight payoff diagrams cover almost every exam strategy question. Long and short futures produce straight 45-degree lines through the entry price. Long calls and puts produce hockey sticks with limited loss and unlimited gain. Short calls and puts produce inverted hockey sticks with limited gain and unlimited or large loss. Combinations build the straddle (V-shape long, inverted V short) and spreads. Being able to sketch each shape from the formula is essential for exam success.

Why it matters

Every payoff shape is built from two pieces, a flat segment where the option expires worthless, and a sloped segment where it pays off. The kink occurs at the strike. The slope is +1+1 for long calls and short puts (positive delta near KK), −1-1 for long puts and short calls (negative delta). Stack two shapes with different strikes or directions and you get every spread on the syllabus. Draw the kinks first, fill in the slopes second.

Formulas

Long call profit
πLC=max⁡(ST−K,0)−C\pi_{\text{LC}} = \max(S_T - K, 0) - C
Flat at −C-C for ST≤KS_T \leq K, then rises one-for-one. Break-even at ST=K+CS_T = K + C.
Short call profit
πSC=C−max⁡(ST−K,0)\pi_{\text{SC}} = C - \max(S_T - K, 0)
Flat at +C+C for ST≤KS_T \leq K, then falls one-for-one. Unlimited loss above KK.
Long put profit
πLP=max⁡(K−ST,0)−P\pi_{\text{LP}} = \max(K - S_T, 0) - P
Rises one-for-one as STS_T falls below KK. Maximum profit at ST=0S_T = 0 equals K−PK - P. Break-even at ST=K−PS_T = K - P.
Short put profit
πSP=P−max⁡(K−ST,0)\pi_{\text{SP}} = P - \max(K - S_T, 0)
Flat at +P+P for ST≥KS_T \geq K, falls one-for-one below KK. Maximum loss at ST=0S_T = 0 equals K−PK - P.
Long straddle profit (same $K$)
πstraddle=max⁡(ST−K,0)+max⁡(K−ST,0)−C−P\pi_{\text{straddle}} = \max(S_T - K, 0) + \max(K - S_T, 0) - C - P
V-shape with apex at ST=KS_T = K where loss equals −(C+P)-(C + P). Two break-evens at K±(C+P)K \pm (C + P).

Worked examples

Scenario

Sketch the long call profit. CBA 6-month European call, strike K=K = A$100, premium C=C = A$5.

Solution

On the horizontal axis put STS_T. On the vertical axis put profit. Draw a flat horizontal segment at −5-5 for all ST≤100S_T \leq 100. From ST=100S_T = 100 onwards draw a line rising at slope $1$. The line crosses zero at ST=105S_T = 105 (the break-even, K+CK + C). For every dollar above 105 the profit grows by one dollar, with no upper bound.

Scenario

Sketch the short put profit. ANZ 3-month European put, strike K=K = A$30, premium P=P = A$1.50.

Solution

Flat at +1.50+1.50 for ST≥30S_T \geq 30, sloping downward at −1-1 as STS_T falls below 30. Break-even at ST=30−1.50=28.50S_T = 30 - 1.50 = 28.50. Maximum loss at ST=0S_T = 0 equals $30 - 1.50 = 28.50$. The inverted hockey-stick shows why short puts are sometimes called 'getting paid to buy the stock cheap'.

Common mistakes

  • ✗Payoff and profit diagrams are the same. Payoff ignores the premium and shows max⁡(ST−K,0)\max(S_T - K, 0) or max⁡(K−ST,0)\max(K - S_T, 0). Profit is the payoff minus the premium for long positions, or plus the premium for short positions. The profit curve is the payoff shifted vertically.
  • ✗Short puts have unlimited loss. Loss is bounded because STS_T cannot fall below zero. Maximum short-put loss equals K−PK - P per share. Short calls do have effectively unlimited loss because STS_T has no theoretical ceiling.
  • ✗A straddle is the same as a strangle. A straddle uses the same strike for the call and put. A strangle uses different strikes (call strike above put strike), making it cheaper but requiring a larger move to break even.

Revision bullets

  • •Futures: straight 45-degree lines through F0F_0
  • •Long call/put: hockey stick, limited loss = premium
  • •Short call/put: inverted hockey stick, capped gain = premium
  • •Long straddle: V-shape, profits on large move either way
  • •Always sketch the kink at the strike first
  • •Profit = payoff - premium for long positions

Quick check

A long put profit diagram is:

The break-even price for a long call with strike K=K = A$50 and premium C=C = A$3 is:

Connected topics

Long CallShort CallLong PutShort PutKey Formulas

In learning paths

Exam Revision Path

Sources

  1. Hull (2022), Ch. 12
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Chapter 12 presents the standard payoff and profit diagrams for single-option positions and combinations.
  2. Hull (2022), Ch. 1, futures payoffs
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022.
    Section 1.4 covers long and short futures payoff diagrams as the simplest 45-degree-line case.
  3. OIC, Strategy diagrams
    Options Industry Council. Options Strategy Library. OIC Education.
    Industry reference with annotated payoff and profit diagrams for every standard option strategy.
  4. McDonald (2013), Derivatives Markets, Ch. 3
    McDonald, Robert L. Derivatives Markets. 3rd ed. Pearson, 2013. ISBN 978-0-321-54308-0.
    Alternative undergraduate textbook with detailed treatment of insurance, spread, and combination payoff shapes.
How to cite this page
Dr. Phil's Quant Lab. (2026). Common Payoff Shapes. Derivatives Atlas. https://phucnguyenvan.com/concept/revision-payoffs
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