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.

4 min read · 648 words · Updated

1 · SnapshotThe one idea to remember
Key intuition: a digital converts "how far will it go?" into pure "will it or won't it?" — the market's odds on an event, bottled and tradable.
2 · 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.

European digital call: nothing below the strike, a fixed cash amount above it.
KDigital callSpot at expiryPayoff

Point at a line to pick it out from the others.

Asset class
FX derivatives
Instrument type
Binary-payout option
Traded
OTC interbank (retail versions widely banned)
Typical users
Macro funds, exotics desks, structurers

Which risks decide the outcome

Not how risky this is, and not a rating — there is deliberately no total. It says which of five failure modes drives what happens here, in the same order on all 129 products so they can be compared. This publication's own reading; see the notice below.

  • Marketdecides it
  • Creditmatters
  • Liquiditybarely applies
  • Fundingbarely applies
  • Operationalmatters

What decides it here. All or nothing at one moment, so the final minutes carry the entire payoff and a small move decides everything.

What the five mean, and which one decides where →

3 · 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.

Worked example: ahead of a central-bank decision, a fund buys a one-week digital paying €5M if EUR/USD ends above 1.12 (spot 1.1150), costing €1.9M — implied odds ~38%. The hawkish surprise lands, spot ends 1.1230: payout €5M, a 2.6x return on a view that "spot up half a percent" would barely have paid via vanillas.
4 · AdvancedPricing & valuation

Pricing and the skew correction

Under Black–Scholes a cash-or-nothing call paying 1 is simply the risk-neutral probability:

$$ D = e^{-r_d T} N(d_2) $$
What the symbols mean
  • Dduration: how far a bond's cash flows sit in the future
  • rthe interest rate, per year
  • Tmaturity, in years
  • Nthe normal distribution, or a count

But differentiating the real (smile-affected) call price by strike gives the model-free value:

$$ D = -\frac{\partial C}{\partial K} = e^{-r_d T}\Big[N(d_2) + \sigma'(K)\, S\sqrt{T}\, \varphi(d_1)\Big] $$
What the symbols mean
  • Dduration: how far a bond's cash flows sit in the future
  • Cthe price of a call option
  • Kthe strike: the price written into the contract
  • rthe interest rate, per year
  • Tmaturity, in years
  • Nthe normal distribution, or a count

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.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.

5 · Desk notesHow practitioners think about it
Practitioner note: quoting a digital = quoting the smile's slope; quoting a one-touch = quoting the smile's dynamics. The two products together tell you almost everything a dealer's model believes about a currency.

Now say it back

Close the page and give FX Digital Option in four sentences. It takes a minute and it is the only way to find out whether reading it was enough.

  1. Who wants what — two parties wanted opposite things badly enough to write it down.
  2. What the contract obliges, and when — not the payoff; the obligation.
  3. Where the money comes from — name the source, or you have described a hope.
  4. What makes it lose — the ordinary way, not the dramatic one.

Do it with a clock → · why these four

Put FX Digital Option beside any other instrument →

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Where this instrument shows up elsewhere

  • MediumWhich Desk Trades WhatPrepEleven trading seats and six that sit next to them: what each one actually touches, the single number it lives by,…

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