Payoff diagrams: long and short calls and puts at expiry

What you will learn

• The difference between a payoff and a profit-and-loss profile
• The shape of the four basic positions: long call, short call, long put, short put
• How to read maximum profit, maximum loss and break-even from a payoff table
• Why short options have a limited gain and a large possible loss

Explanation

A payoff diagram shows the value of a position at expiry for every possible price of the underlying. The horizontal axis is the underlying price at expiry, the vertical axis is the result. Strictly, the payoff is the option's value at expiry, and the profit and loss (P&L) is the payoff minus the premium paid (or plus the premium received). In this lesson we show P&L per share, because that is what matters for a decision.

You can draw each diagram with just three points: one far below the strike, the strike itself and one far above it. The line bends ("kinks") only at the strike.

The four basic positions (per share, at expiry)

S = price at expiry, K = strike, P = premium per share.

Each short position is the mirror image of the long position: the same line flipped around the zero axis. What the buyer wins, the seller loses, before costs.

Shapes in words:

• Long call: flat at −P below the strike, then rising one-for-one.
• Short call: flat at +P below the strike, then falling one-for-one without a limit.
• Long put: falling one-for-one until the strike, then flat at −P.
• Short put: rising until the strike, then flat at +P. Its shape looks like owning shares with a capped upside.

Short options often win small amounts frequently and occasionally lose large amounts. A long series of small gains says little about the risk of the position; the risk is in the tail.

Worked example

Hypothetical example: a share trades at €100. A call with strike €100 costs €4.00, a put with strike €100 costs €3.00 (same expiry). Results per share at expiry, no fees, no margin interest. Multiply by the contract multiplier (for example 100) for the money result.

Example calculation for the long call at €110: max(€110 − €100, 0) − €4 = €10 − €4 = €6.00. With multiplier 100, that is €600.

Reading the table: the long call's loss is capped at €4.00 per share (€400 per contract), but the short call keeps losing as the price rises. At €150 the short call would lose €50 − €4 = €46 per share, €4,600 per contract, for a maximum gain of €400. The short put's worst case is the share falling to zero: €100 − €3 = €97 per share, or €9,700 per contract.

Common mistake

Practice activity

Hypothetical: you sell 1 put with strike €50 for a premium of €2.50, multiplier 100. Ignore fees and margin interest.

1. Calculate the P&L per contract at expiry for share prices of €40, €47.50, €50 and €60.
2. State the break-even, the maximum profit and the maximum loss per contract.
3. Describe the shape of the diagram in one sentence.

Key takeaways

• Payoff diagrams show results at expiry; they bend only at the strike.
• Long options: limited loss (the premium). Short options: limited gain (the premium).
• A short call has unlimited loss; a short put can lose the strike minus premium.
• Expiry diagrams do not show the P&L before expiry.

Next step

In the next lesson you will learn the Greeks, which describe how an option price changes before expiry when the underlying, time and volatility change.