The payoff of an option at expiration is determined by the relationship between the stock price and the strike price. The payoff is the gross amount received before accounting for the premium paid or received. The profit or loss is the payoff minus the premium for long positions, or the payoff plus the premium for short positions.

For a long call, the payoff is max(0, Stock - Strike) per share. You profit when the stock exceeds the breakeven (strike plus premium). For a long put, the payoff is max(0, Strike - Stock) per share. You profit when the stock falls below the breakeven (strike minus premium). Short positions reverse these calculations: you receive the premium upfront and your payoff is negative when the option is in the money.

The ROI (return on investment) measures the percentage return relative to the premium. For long positions, ROI = profit / premium paid. For short positions, ROI = profit / premium received. Each contract represents 100 shares, so all per-share values are multiplied by 100 and then by the number of contracts to determine total dollar amounts.

Formulas

Long Call Payoff = max(0, Stock - Strike) × 100 × Contracts

Long Put Payoff = max(0, Strike - Stock) × 100 × Contracts

Long P&L = Payoff - Premium × 100 × Contracts

Short P&L = Premium × 100 × Contracts - Payoff

Call Breakeven = Strike + Premium

Put Breakeven = Strike - Premium

Example

You buy a $100 call for $4.00 on 1 contract. At expiry the stock is $110. Payoff is ($110 - $100) × 100 = $1,000. Profit is $1,000 - ($4.00 × 100) = $600. Breakeven is $100 + $4.00 = $104. ROI is $600 / $400 = 150%.