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Key Takeaways
- A cash-or-nothing binary pays a fixed amount when its stated settlement condition is met and zero otherwise.
- The example pays $100 when the settlement value is strictly above 100 and zero at or below 100.
- A $40 purchase produces either $60 profit or $40 loss at settlement.
- A binary’s price divided by its payout is the discounted risk-neutral probability of the event: $40 on a $100 payout prices it at 40% at zero rates.
- A narrow call spread has a ramp between its strikes; its expiration breakeven determines where that spread becomes profitable.
What is a binary option?
A binary option, also called a digital or all-or-nothing option, is a contract that pays all or nothing on a specified condition; the cash-or-nothing type pays a fixed amount when the condition is met and zero otherwise. The cash-or-nothing example on this page costs $40 and pays $100 if the settlement value is strictly above 100. A value at or below 100 pays zero.
The resulting expiration profit is $60 in the winning outcome and a $40 loss in the other outcome. Finishing at 100.05 or 118 produces the same payout. The contract’s reference value, observation time and equality rule determine settlement.
Other digital structures define different triggers or deliver an asset instead of fixed cash. Read the payoff and observation terms for the specific contract being evaluated.
Binary option pricing and risk-neutral probability
For a European cash-or-nothing call under Black-Scholes, value equals fixed payout times exp(-rT) times N(d2). N(d2) is the risk-neutral probability that the underlying finishes above the threshold under that model.
Divide value by payout and multiply by exp(rT) to recover that probability. At zero rates, $40 divided by $100 gives 40%. At a 5% continuously compounded rate and one year remaining, the corresponding probability is 42.05%.
Formula
Cash-or-nothing call payoff = Q × 1{S_T > K}; European Black-Scholes value V = Q × exp(−rT) × N(d₂); risk-neutral probability = (V / Q) × exp(rT)- Q is the fixed cash payout, K the threshold, and S_T the specified settlement value.
- For this European Black-Scholes model, d₂ = [ln(S/K) + (r − q − σ²/2)T] / (σ√T).
- r is the continuously compounded interest rate, q the continuous dividend yield, σ the volatility and T the remaining years.
- At zero rates V/Q is the probability itself; at any other rate, multiply V/Q by exp(rT) to remove the discounting.
Worked Example
A cash-or-nothing binary call on an index settles at $100 per contract if the index finishes above 100 and at $0 if it finishes at or below 100. The contract is quoted at $40.
- Binary entry price: $40; winning settlement: $100; net winning profit: $60
- At 100.05 or 118.00: binary payout $100 and profit $60
- At 100.00 or 99.95: binary payout $0 and loss $40
- One standard 99.50/100.50 call spread entered for $0.40 costs $40 and has $100 maximum expiration value
- The spread breaks even at 99.90 and has $10 profit at settlement 100.00
The binary has two settlement outcomes. The spread ramps between 99.50 and 100.50, becoming profitable above 99.90. At exactly 100, the binary loses $40 while the spread earns $10. Calculate each position against its own payoff and breakeven.
Binary option vs a narrow call spread
Buy one standard 99.50 call for $0.75 and sell one 100.50 call for $0.35. The $0.40 debit costs $40, and the $1 width has $100 maximum expiration value. Maximum expiration profit is $60 and breakeven is 99.90.
At settlement 100, the spread is worth $50 and earns $10. The binary’s strict-above condition fails at that exact value, so it loses $40. Between the spread strikes, calculate the ramp directly.
For a narrowing, scaled spread, the payoff approaches the binary’s step away from the threshold, and the contract’s equality rule settles the threshold itself. A call spread’s price divided by its width is a discounted probability too, averaged across the strikes between its legs.
The spread’s probability of profit instead uses its 99.90 breakeven. Build the vertical in the options profit calculator to compare the actual dollar outcomes at each target price.
Where do regulated binary options trade in the US?
In the US, regulated binary contracts trade on securities exchanges or on CFTC designated contract markets, each under its own market rules. Use the SEC exchange records or CFTC designated-contract-market records to identify the venue. Read the listed contract’s threshold, observation time and settlement procedure before comparing it with another structure.
Limitations of binary options
- Use a binary when only the side of the finish matters. A cash-or-nothing payoff is a step: a settlement value just on the wrong side of the threshold loses the full premium, and a value far past it earns no more than a value just past it. The example pays the same $100 at 100.05 and 118, and loses $40 at exactly 100.
- Read the exact settlement terms: reference value, observation time and equality rule. Two contracts with the same threshold can settle differently.
- Price divided by payout is the probability the price charges, discounted for time. At zero rates the $40 binary on a $100 payout breaks even over many trades when the event happens 40% of the time, so buy it only when your own odds are higher.
- Trade binaries on a regulated US venue. Binary options sold through off-exchange websites can fall outside US regulation, and the SEC, CFTC and FINRA have warned investors about fraudulent schemes on such platforms.
Bottom line
A cash-or-nothing binary option turns a yes-or-no condition into two outcomes: a fixed payout if the stated condition holds and nothing if it does not. Read the threshold, observation time and equality rule before trading, weigh price divided by payout, the probability the price charges, against your own odds, and confirm the venue through SEC exchange or CFTC designated-contract-market records.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- CFTC: Beware of Off-Exchange Binary Options Trades
- CFTC: Understanding Prediction Markets and Event Contracts
- SEC Investor Alert: Binary Options Websites May Be Used for Fraudulent Schemes
- FINRA: Regulators Warn Investors of Binary Options Risks
- OCC: Characteristics and Risks of Standardized Options (Options Disclosure Document)
How entries are sourced, calculated and updated: editorial methodology.