Derivatives13 min readUpdated June 2026

Derivatives Payoffs in 8 Diagrams

Options payoffs are tested across nearly every finance exam — ICWIM Chapter 3, CFA Level 1, CISI Diploma Unit 4, and dedicated derivatives papers. The payoffs themselves are simple geometry once you've seen them. This guide visualises the 8 most-tested positions with formulas, break-evens, and the exam traps for each.

How to read each diagram. The x-axis shows the underlying price at expiry; the y-axis shows the profit or loss of the position at expiry (after premium paid/received). The dashed vertical line marks the strike price. Above zero = profit; below zero = loss.

1. Long Call

You buy a call option for premium p, with strike K. If at expiry the underlying is above K, you exercise and pocket the difference. If below, the option expires worthless and you lose only the premium.

Long Call — bullish, limited downside, unlimited upside
K BE 0 -p Spot P/L
Max profit: Unlimited  ·  Max loss: Premium paid (p)  ·  Break-even: K + p

2. Long Put

You buy a put option for premium p, with strike K. If the underlying falls below K by expiry, you exercise (sell at K, buy back at the low spot). If it stays above, the put expires worthless.

Long Put — bearish, limited downside, large but capped upside
K BE 0 -p Spot P/L
Max profit: K − p (if spot → 0)  ·  Max loss: Premium paid (p)  ·  Break-even: K − p

3. Short Call (Naked)

You sell (write) a call option, collecting premium p upfront. If the underlying stays below K, the option expires worthless and you keep p. If it rises above K, your losses are theoretically unlimited.

Short Call — neutral/bearish, limited upside, unlimited downside
K BE 0 +p Spot P/L
Max profit: Premium received (p)  ·  Max loss: Unlimited  ·  Break-even: K + p  ·  Margin required (uncovered).

4. Short Put

You sell a put option, collecting premium p. If the underlying stays above K, you keep p. If it falls below K, you're obliged to buy at K — losses grow as spot falls (capped only when spot reaches zero).

Short Put — neutral/bullish, large downside if spot falls, capped upside
K BE 0 +p Spot P/L
Max profit: Premium received (p)  ·  Max loss: K − p (if spot → 0)  ·  Break-even: K − p

5. Covered Call

You own the underlying AND write a call against it. You collect the premium p and cap your upside at K. The strategy generates income from stocks you'd be willing to sell at K anyway.

Covered Call — capped upside in exchange for premium income
K 0 +max Spot P/L
Max profit: (K − S0) + p  ·  Max loss: S0 − p (if spot → 0)  ·  Use case: Income generation on a stock you're willing to sell at K.

6. Protective Put

You own the underlying AND buy a put option as insurance. You pay premium p for downside protection at strike K. The combination behaves like a long call with full upside but capped downside.

Protective Put — full upside with downside floor (insurance)
K 0 floor Spot P/L
Max profit: Unlimited  ·  Max loss: (S0 − K) + p  ·  Behaves like: A long call (synthetic equivalent).

7. Long Straddle

You buy a call AND a put at the same strike K. You profit if the underlying moves significantly in either direction. Used when expecting volatility but unsure of direction (around earnings, central-bank announcements).

Long Straddle — profits on big moves either way (long volatility)
K BE BE 0 -2p Spot P/L
Max profit: Unlimited (either direction)  ·  Max loss: Total premium (pcall + pput)  ·  Break-even: K ± total premium

8. Bull Call Spread

You buy a lower-strike call (K1) AND sell a higher-strike call (K2). Profit is capped between strikes, loss capped at net premium paid. Lower cost than a single long call, but you give up the upside beyond K2.

Bull Call Spread — capped upside & downside, cheaper than naked long call
K₁ K₂ 0 -net p +max Spot P/L
Max profit: (K2 − K1) − net premium  ·  Max loss: Net premium paid  ·  Break-even: K1 + net premium

Put-call parity (essential formula)

For European options on a non-dividend-paying stock:

C + Ke-rT = P + S0

Where C = call price, P = put price, K = strike, T = time to expiry, r = risk-free rate, S0 = current spot.

This identity lets you derive synthetic positions. For example, a protective put (S0 + P) equals a long call plus risk-free bond (C + Ke-rT) — which is why the protective put payoff looks like a long call.

Most-tested exam traps

ConfusionThe fix
Confusing payoff with profit Payoff = value at expiry. Profit = payoff − initial cost (premium). Most exam questions ask about PROFIT.
Mixing "long" and "short" terminology Long = bought. Short = sold/wrote. Long call ≠ long stock. Long call + short stock IS sometimes a synthetic position.
Covered call vs naked call Covered = you own the underlying (max loss limited). Naked = you don't (theoretically unlimited loss).
Bull spread direction Bull = profits as price RISES. Done with calls (buy lower / sell higher) OR puts (sell higher / buy lower). Reverse for bear.
Straddle vs strangle Straddle = same strike. Strangle = different strikes (call higher, put lower). Strangle is cheaper but needs a bigger move to profit.
Forward vs futures Forwards = OTC, bespoke, no daily margining. Futures = exchange-traded, standardised, daily margining (mark-to-market).
American vs European American = exercisable any time before expiry. European = only at expiry. American calls on non-dividend stocks behave like European (never optimal to early-exercise).

Drill these in the ICWIM Q bank

icwim.com's ICWIM Ch 3 (Asset Classes & Markets) has 83+ practice questions, many testing exactly these payoff scenarios. Plus the Calculation Drill mode focuses just on the maths.

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