Binary Options

A binary option, also called a digital option, pays a fixed amount if a condition is true at expiration and nothing if it is false. A typical example pays $100 if a stock closes above $50 on Friday and $0 otherwise. Unlike a standard option, the payoff does not grow with the size of the move; it is all or nothing. Binary options exist as legitimate instruments on regulated exchanges and inside bank structured products, but the term is also tied to a long history of offshore fraud, so it is important to know the difference.

Types of binary options#

One touch and no touch options are barrier style binaries, popular in FX markets. See Barrier Options.

Pricing#

Under Black Scholes assumptions, a cash or nothing call paying $1 is worth:

binary call = e^(-rT) × N(d2)

N(d2) is the risk neutral probability that the option finishes in the money, so the binary's price is essentially the discounted probability of the event. See Black-Scholes Model.

Binary options and prediction markets#

Prediction market contracts work like binary options: a share pays $1 if an event happens and $0 if not, and its price reflects the probability. Polymarket's crypto up or down markets are effectively short dated binary options on whether a coin finishes above its starting price. See What Are Prediction Markets? and Up or Down Markets Explained.

In the United States, regulated venues such as Nadex (now Crypto.com | Derivatives North America) and CME list binary style event contracts under CFTC oversight.

Hedging and the strike problem#

Binary options are hard to hedge near expiry. With little time left and the price near the strike, the value can jump between almost $0 and almost the full payout on a tiny move, so delta and gamma become extreme. Dealers often approximate binaries with tight call spreads to manage this risk, which means binaries are effectively priced using the skew of nearby vanilla options. See Gamma and Volatility Smile and Skew.

The binary options scam problem#

In the 2010s, many unregulated offshore websites offered "binary options" to retail customers. Regulators found widespread fraud:

• Platforms that manipulated prices or refused withdrawals.
• Payouts structured so that customers lost on average, even before manipulation.
• Aggressive sales tactics and fake testimonials.

The European Securities and Markets Authority banned the marketing, distribution and sale of binary options to retail clients across the EU in 2018, and other regulators issued similar bans or warnings. The SEC and CFTC have published investor alerts about binary options fraud. See Identifying Trading Scams.

Common mistakes#

• Ignoring the payout structure: many retail platforms paid 70% to 85% on a win but took 100% on a loss, which loses money at a 50% win rate.
• Trading very short expiries that are close to random.
• Using unregulated platforms.

Frequently asked questions#

What is a binary option?#

An option that pays a fixed amount if a condition is met at expiry, such as the price being above a strike, and nothing otherwise.

Are binary options legal?#

It depends on the country and venue. They are banned for retail clients in the EU and restricted elsewhere, while some regulated US exchanges list binary style contracts.

How are binary options priced?#

Their price is close to the discounted probability of the event happening; under Black Scholes, a $1 binary call is worth e^(minus rT) × N(d2).

Next, learn average price options in Asian Options.

Sources#

• SEC and CFTC, Investor alert: binary options and fraud
• Wikipedia, Binary option