Long Call and Short Call: Option Payoff Diagrams Explained
The long call payoff is max(ST-K,0) minus premium. The short call is the exact negative. Worked numerical example with K=$95 and payoff tables for both positions.
The futures payoff formula is ST minus K. Plug in any stock price and you get the profit or loss. There is no decision to make.
Options add one extra step: the buyer decides at expiry whether to execute. That one extra step is why the payoff diagram has a kink instead of a straight line.
Understanding where that kink falls, and what causes it, is the first thing options analysis asks of you.
The Expectations Behind Each Position
Four positions are possible in option markets. Each one reflects a specific directional expectation.
Long call (buying the right to buy): you expect the price to rise. You are bullish. You paid premium for the right to buy, and you exercise only if the price exceeds the strike at expiry.
Short call (selling the right to buy): you expect the price to fall or stay flat. You are bearish. You received premium, but if the buyer exercises, you must sell the underlying at the strike price regardless of what the market offers.
Long put (buying the right to sell): you expect the price to fall. You are bearish. If the price drops below the strike at expiry, you exercise and sell at the higher predetermined price.
Short put (selling the right to sell): you expect the price to rise or stay flat. You are bullish. You received premium, and if the buyer exercises, you must buy the underlying at the strike price.
A memory technique: think of a bull throwing its horns upward, and a bear swiping its claws downward. Bullish means expecting a rise. Bearish means expecting a decline.
Long call and short put are bullish positions. Short call and long put are bearish positions.
Premium: The Constant Rule
One rule applies to every option in every market.
The long position always pays premium. The short position always receives it.
The buyer of an option is called the holder. The seller is called the underwriter. The holder has the freedom to walk away at expiry; the underwriter does not. Whatever the holder decides, the underwriter must honor. That asymmetry has a price: the holder pays it upfront as premium to compensate the underwriter for bearing the obligation with no exit.
Long Call Payoff
The Equation
The long call payoff formula is max(ST - K, 0) - premium, where ST is the stock price at expiry and K is the strike price.
The max() function captures the buyer's choice. If ST is above K, the holder exercises and earns ST - K. If ST is below K, the holder walks away and the exercise value is zero.
Either way, the premium was already paid upfront and is always subtracted.
Long Call: K = $95, Premium = $1
| ST | max(ST - 95, 0) | Payoff (- $1 premium) |
|---|---|---|
| $90 | 0 | -$1 |
| $91 | 0 | -$1 |
| $92 | 0 | -$1 |
| $93 | 0 | -$1 |
| $94 | 0 | -$1 |
| $95 | 0 | -$1 |
| $96 | $1 | $0 |
| $97 | $2 | $1 |
| $98 | $3 | $2 |
| $99 | $4 | $3 |
| $100 | $5 | $4 |
From $90 to $95, the holder does not exercise. Payoff is flat at -$1. The premium paid is the only cost, and nothing recovers it below the strike.
At $96, payoff is exactly $0. This is the break-even point.
Above $96, payoff rises linearly with every dollar the stock climbs.
Break-even = K + premium = $95 + $1 = $96.
The Shape
The long call diagram has two segments: a flat line at -premium for all prices below the strike, and a rising line for all prices above the break-even.
Limited loss. Unlimited profit. No matter how far the stock falls, the buyer loses only the premium. No matter how far it rises, the profit has no ceiling.
Short Call Payoff
Short Call Equation
The short call payoff is the exact negative of the long call: premium - max(ST - K, 0).
Whatever the long position gains, the short position loses. Whatever the long loses, the short gains. The seller received premium upfront (positive), but must pay out any intrinsic value the buyer earns.
Short Call: K = $95, Premium = $1
| ST | max(ST - 95, 0) | Payoff ($1 premium - above) |
|---|---|---|
| $90 | 0 | +$1 |
| $91 | 0 | +$1 |
| $92 | 0 | +$1 |
| $93 | 0 | +$1 |
| $94 | 0 | +$1 |
| $95 | 0 | +$1 |
| $96 | $1 | $0 |
| $97 | $2 | -$1 |
| $98 | $3 | -$2 |
| $99 | $4 | -$3 |
| $100 | $5 | -$4 |
From $90 to $95, the buyer does not exercise. The seller keeps the full premium. Payoff is flat at +$1.
At $96, payoff drops to $0 (break-even for the seller too).
Above $96, the seller's losses increase linearly. At $100, the seller has lost $4.
Short Call Shape
The short call diagram is the mirror image of the long call: flat at +premium for all prices below the strike, then a falling line beyond the break-even.
Limited profit. Unlimited loss. No matter how far the stock falls, the seller earns only the premium. But as the stock rises, losses have no ceiling.
Drag the sliders below to see how the payoff curve shifts when you change the strike price or the premium. Switch between all four positions and watch the kink move.
Interactive Option Payoff Explorer
Profit Formula
max(ST − 95, 0) − 1.0
Break-even Price
$96.0
Max Profit
Unlimited
Max Loss
-$1.0
Derivatives Are a Zero-Sum Game
Look at the two tables side by side. At ST = $100: long call is +$4, short call is -$4. At ST = $90: long call is -$1, short call is +$1.
Every dollar gained by the long is an identical dollar lost by the short.
This is why derivatives are called a zero-sum game. No wealth is created or destroyed between the two parties. Money transfers from one position to the other, always in equal and opposite amounts.
This holds across every derivative: forwards, futures, and options. The net payoff between any two parties on opposite sides of the same contract always sums to zero.
It also explains why the short call payoff equation is simply the negative of the long call equation. No separate calculation is needed: just flip the sign.
The Essentials
- Long call: limited loss, unlimited profit. The buyer loses at most the premium if the stock stays below the strike. Every dollar the stock rises above the break-even is a dollar of profit.
- Short call: limited profit, unlimited loss. The seller earns at most the premium received. Every dollar the stock rises above the break-even is a dollar of loss.
- Break-even = K + premium. The long call holder needs the stock to clear the strike by at least the premium paid to recover costs. The short call seller starts losing at exactly that same point.
- Derivatives are a zero-sum game. Short call payoff is always the negative of long call payoff. One party's gain is the other party's loss, in exactly equal amounts.
The diagrams for put options follow the same equations but work in the opposite direction. A long put profits when the stock falls below the strike, a short put profits when it stays above. The next post draws those diagrams and introduces the concept of moneyness: whether a position is in the money, at the money, or out of the money, and why it matters.
Further Reading
- Book: Options, Futures, and Other Derivatives by John C. Hull
- Wikipedia: Call option · Option (finance) · Zero-sum game
Keep reading