Four-leg fixed-payoff options strategy
Box Spread Calculator
Calculate a long or short box spread, including the fixed expiration settlement, net debit or credit, profit or loss, implied financing rate and value versus a benchmark interest rate.
| Stock price at expiration | Call-spread payoff | Put-spread payoff | Total option payoff | Net P/L |
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A box has a theoretically fixed expiration value only when all four options share the same underlying, expiration and exercise terms. American-style options can be assigned early. Execution risk, bid/ask spreads, dividends, borrowing costs, settlement rules, taxes and fees can materially change the result.
What a box spread calculates
A long box combines a bull call spread and a bear put spread with the same lower and upper strikes. It buys the lower-strike call, sells the upper-strike call, buys the upper-strike put and sells the lower-strike put. At expiration the two vertical spreads together settle for the strike width, regardless of the underlying price.
A short box reverses all four legs. It receives a credit when opened and owes the fixed strike-width settlement at expiration. Traders often compare the box price with the present value of that settlement to study an implied lending or borrowing rate. The calculator consolidates box spread, long box, short box, arbitrage and implied financing calculations in one URL.
Box spread formulas
Gross box price per share = lower call − upper call + upper put − lower put
Fixed settlement = strike width × spreads × multiplier
Long box net debit = gross box price × shares + fees
Long expiration P/L = fixed settlement − net debit
Short box net credit = gross box price × shares − fees
Short expiration P/L = net credit − fixed settlement
Simple annualized rate = (fixed settlement ÷ entry cash flow − 1) × 365 ÷ days
Effective annual rate = (fixed settlement ÷ entry cash flow)^(365 ÷ days) − 1
Benchmark present value = fixed settlement ÷ (1 + benchmark rate)^(days ÷ 365)
Verified example
With strikes US$95 and US$105, premiums US$8.20 for the lower call, US$3.30 for the upper call, US$7.10 for the upper put and US$2.20 for the lower put, the gross box price is US$9.80 per share. One 100-share long box with US$4 of total fees costs US$984 and settles for US$1,000 after 90 days. Its expiration profit is US$16, simple annualized yield is 6.5944% and effective annual yield is 6.7600%. At a 5% benchmark rate, the settlement has a present value of about US$988.04, giving the long box a US$4.04 pricing edge after fees.
Long box versus short box
- Long box: pays a debit now and receives the fixed strike-width amount at expiration, similar to lending.
- Short box: receives a credit now and pays the fixed amount at expiration, similar to borrowing.
- Pricing edge: for a long box, benchmark present value minus net debit; for a short box, net credit minus benchmark present value.
- Not risk-free in practice: assignment, exercise, execution, tax and settlement details can invalidate a textbook arbitrage.
Limits and assumptions
All premiums are entered per share in the selected display currency; no foreign-exchange conversion is performed. The four legs must use the same expiration, multiplier and underlying. The calculator models expiration cash flows and an annualized rate from calendar days, not a live trade quote or guaranteed borrowing rate.
Inputs are limited to 100,000 spreads, 100,000 shares per contract, 1,000,000,000 total shares, 36,500 days, rates from −99% to 1,000%, and monetary values up to 100,000,000 with at most six decimal places. Results are educational estimates, not investment, tax or legal advice.
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