FX Digital Option
Also known as: Binary option, One-touch, European digital
All or nothing: a fixed payout if the rate ends (or trades) beyond a level. Probability, directly priced.
- Asset class
- FX derivatives
- Instrument type
- Binary-payout option
- Traded
- OTC interbank (retail versions widely banned)
- Typical users
- Macro funds, exotics desks, structurers
BeginnerWhat is it, really?
A digital (binary) option pays a fixed amount if a condition is met, and nothing otherwise. A European digital call on EUR/USD at 1.15 pays, say, $1M if the rate finishes above 1.15 at expiry — whether it finishes at 1.1501 or 1.30. A one-touch pays if the level trades even once before expiry.
Digitals strip options down to their probabilistic core: the price of a digital paying 1 is roughly the market's probability of the event happening (in the risk-adjusted sense). Pay 0.30 for a digital on "above 1.15"? The market says ~30%.
A warning that must be said plainly: institutional digitals are legitimate building blocks — but "binary options" sold to retail through online platforms became a global scam industry, and are banned for retail sale in the EU, UK and elsewhere. If a website offers you 5-minute binaries, it is not this product; it is a casino, frequently rigged.
IntermediateHow it works in practice
The family
- European digital (cash-or-nothing): pays on the expiry fixing only.
- One-touch / no-touch: pays if a barrier trades / never trades — the FX exotics market's liquidity benchmark.
- Double-no-touch (DNT): pays if spot stays inside a range — the classic "quiet market" trade.
- Range accruals: coupon accrues per day inside a range — digitals in daily instalments.
Where they're used
- Event trades: elections, referendums, central-bank pivots — clean payouts on scenarios.
- Structured products: most "if the index is above X you get Y" retail notes embed digitals.
- Model calibration: one-touch quotes discipline the smile-dynamics models used for all FX exotics.
Replication intuition
A digital is the limit of a tight call spread: buy a call at 1.1495, sell at 1.1505, scale up — the payoff approaches a step. This is exactly how dealers hedge and price them, and why digital prices inherit the volatility skew: the spread straddles the smile.
AdvancedPricing & valuation
Pricing and the skew correction
Under Black–Scholes a cash-or-nothing call paying 1 is simply the risk-neutral probability:
But differentiating the real (smile-affected) call price by strike gives the model-free value:
The skew-slope term \(\sigma'(K)\) is first-order: on steep smiles, ignoring it misprices digitals by many percentage points. Digital pricing is thus a direct application of Breeden–Litzenberger — the risk-neutral CDF read off the smile.
Touch products need dynamics
One-touch value depends on the path, hence on how the smile moves with spot — the quantity vanilla prices don't pin down. Local vol and stochastic vol give materially different touch prices from identical vanilla fits; desks calibrate LSV mixing to market one-touch quotes (the "touch ladder"), making touches the empirical anchor of FX smile dynamics. Under BS, the undiscounted one-touch has the closed form combining two digitals via the reflection principle.
Hedging a step function
Near expiry near the strike, digital delta is a spike (formally a Dirac limit): unhedgeable pointwise. Dealers hedge the call-spread over-replication — width chosen by risk appetite — booking the spread cost as the price. The wider the spread, the more conservative the quote; payout-at-barrier conventions and fixing-source disputes are the operational risks.