The combined expiration payoff can be fixed under matched contract assumptions. That is not a guarantee of risk-free profit: financing, stock borrow, dividends, early assignment, execution and settlement must also be considered. American-style Box Spreads can be disrupted by early exercise. A price difference alone does not establish an executable arbitrage.
Sell short 100 shares; Sell 1 put; Buy 1 call. Use the same strike price and expiration date.
Matched payoff and financing considerations
Profit = Sale Price of Underlying - Strike Price of Call/Put + Put Premium - Call Premium
Example
Suppose XYZ stock is trading at $100 in June and the JUL 100 call is priced at $3 while the JUL 100 put is priced at $4. An arbitrage trader does a reversal by short selling 100 shares of XYZ for $10000 while simultaneously buying a JUL 100 call for $300 and selling a JUL 100 put for $400. An initial credit of $10100 is received when entering the trade.
If XYZ stock rallies to $110 in July, the short JUL 100 put will expire worthless while the long JUL 100 call expires in the money and is exercised to cover the short stock position for $10000. Since the initial credit received was $10100, the trader ends up with a net profit of $100.
If instead XYZ stock had dropped to $90 in July, the long JUL 100 call will expire worthless while the short JUL 100 put expires in the money and is assigned. The trader then buys back the obligated quantity of stock for $10000 to cover his short stock position, again netting a profit of $100.
These examples use standard U.S. stock options with a 100-share contract size and matching expiration dates. Related structures can use ETF, index or futures options, but contract multipliers, exercise style, settlement and the underlying price range can differ. A stock’s zero price floor must not be assumed for every futures contract.
Commissions
For ease of understanding, these examples exclude commissions, fees and financing costs. Include all costs when comparing an actual position; there is no universal commission amount.
For active traders, transaction costs can consume a significant part of returns. Compare the full commission and fee schedule, exercise and assignment charges, and bid-ask spreads. The cost of entering and closing every leg matters.
Conversion
If the options are relatively overpriced, the Conversion is used instead to perform the arbitrage trade.
Before expiration and assignment
The diagrams and worked outcomes describe expiration payoffs, not an option’s market price before expiration. Time decay, implied volatility, rates, dividends and bid-ask spreads affect early closing values. American-style short options can be assigned early; a protective long option is not automatically exercised when a short leg is assigned. Closing or exercising one leg can change the remaining position’s risk.
Payoff summary
Maximum profit: Zero minus strike price minus net opening cost.
Maximum loss: Strike price plus net opening cost.
Breakeven
The position breaks even at every stock price only when the net opening cost equals zero minus strike price. Otherwise, there is no breakeven stock price.
Net opening cost means everything paid to open the position, less everything received. Include the shares as well as the options. If opening the position brings in money overall, treat that cost as a negative amount.
Amounts are per share before fees. Multiply by the shares covered by the position; standard equity options usually cover 100 shares per contract. If a maximum profit or loss calculation gives a negative amount, use zero. These figures assume matching contracts held to expiration and do not include financing or early assignment.
