The article below contains advanced math to explain why binary options are designed to benefit the broker selling them. If you prefer a more down to earth introduction to binary options the I recommend you visit BinaryOptions.net. They will tell you everything you need to know to understand binary options.

A conventional binary option is a two-state contingent claim with a fixed terminal payoff. At expiry T, a contract linked to an observable X_T (e.g., an asset price, index level, or event outcome) returns 1 unit if a Boolean condition is satisfied and 0 otherwise. For example, an “up” (call) binary pays 1 if X_T ≥ K and 0 if not.

Payoff at T:  Π_T = 𝟙{ X_T ≥ K }

Display Convention (0–100 Scale)

Prices are often displayed on a 0–100 scale for convenience. A quoted “price = 37” corresponds to a monetary outlay of 0.37 to receive 1.00 if the condition is true (and 0 otherwise). In probability terms, a fair value of p maps to a display price of 100 × p.

Display price ↔ probability:  price = 100·p   ↔   p = price / 100

In frictionless markets with complete information, the no-arbitrage value equals the risk-neutral probability of the event, discounted appropriately. Real-world platforms are not frictionless, as quotes embed spreads and fees, and execution is path-dependent near expiry Those frictions shift the expected value of a typical retail trade below zero even when the trader’s directional accuracy is near 50–55%.

The seller of a retail binary option is commonly the platform or its market maker, adding a conflict of interest.

Formal payoff and fair value

Payoff at Maturity

Consider a digital (cash-or-nothing) call option with strike K and maturity T. The payoff is

Π_T = 𝟙{ S_T ≥ K }

Arbitrage-Free Price (Time t)

Under Black–Scholes assumptions, the arbitrage-free value at time t is

V_t = e^−r τ N(d₂),   with   τ = T − t

d₂ = [ ln(S_t/K) + ( r − ½ σ² ) τ ] / ( σ √τ )

where r is the risk-free rate, σ is volatility, N(·) is the standard normal CDF, and S_t is the underlying price at time t. This “fair” price equals the (risk-neutral) exercise probability discounted to present value.

Retail Platform Quotes

Retail customers typically face a spread/fee around the fair value:

• Buy price (quote to purchase the digital): B = V_t + Δ
• Sell price (quote to sell back): A = V_t − Δ

Here, Δ > 0 is the half-spread (captures margin/fees embedded in quotes).

Expected P&L for a Buyer

Let p = P(S_T ≥ K) be the buyer’s (objective) exercise probability and let c denote explicit fees. If the trader buys one unit at price B, then single-trade expected P&L is

E[P&L | buy at B] = p · (1 − B) + (1 − p) · (0 − B) − c = p − B − c.

Implication Under “Correct” Beliefs

If the trader’s belief equals the platform’s risk-neutral probability (so B = p + Δ), then

E[P&L] = p − (p + Δ) − c = −(Δ + c) < 0.

Therefore, even perfect calibration of p is insufficient: to earn positive expected value after costs, the trader must consistently forecast exercise probabilities that exceed the market’s by more than Δ + c. Short expiries typically increase Δ relative to signal, raising the hurdle.

Note (related payoff): Asset-or-Nothing Call

For comparison, an asset-or-nothing call pays S_T 𝟙{S_T ≥ K} and has Black–Scholes price S_t N(d₁), where d₁ = d₂ + σ√τ.

All-or-nothing payoff concentrates error

Binary options collapse magnitude and timing into a single terminal tick. Being “nearly right” yields the same 0 payoff as being completely wrong. Near maturity, small shocks to S_t cause large changes in N(d₂) (gamma of the digital grows as τ→0), making quoted “probabilities” hypersensitive to microstructure noise and last-print idiosyncrasies. This steep mapping amplifies slippage and timing error. Two orders submitted seconds apart can face materially different fair values, while both still pay the same spread. For retail users, this sensitivity degrades realized expectancy.

Example

Let’s say you’re trading a binary option on whether a stock will close above $100 by 3:00 PM. The option pays $1 if it does, $0 if it doesn’t.

It is now 2:59:50 PM (ten seconds left to expiry), and the stock is bouncing between $100.02 and $99.98 , i.e. just a few cents difference. Because the outcome depends entirely on whether it’s above or below $100 at exactly 3:00 PM, those tiny price wiggles cause the market’s “probability” to swing dramatically.

When the stock price is $100.02, the market´s implied probability (option price) is 0.60 (60%).

When the stock price is $99.98, the market´s implied probability (option price) is 0.40 (40%).

The is a 20-point swing from just 4 cents of movement.

If you place your order when the price is $100.02, you might pay 0.60. But if the price ticks down to $99.98 a few seconds later, that same bet would only be worth 0.40, even though nothing major changed. Yet both trades pay the same fees and spreads, you’re just at the mercy of timing and tiny random fluctuations. Over many trades, this kind of noise and slippage eats away at your profits and makes it very hard for retail traders to come out ahead.

Binary options are “all-or-nothing” bets: you either get paid if the event happens, or you lose the entire stake if it doesn’t. There’s no partial credit for being close. Because of that all-or-nothing nature, timing becomes extremely important. As the option gets close to its expiration (the moment when the bet settles), tiny changes in the underlying price can completely flip the outcome, from “win” to “lose.” In market terms, that means the quoted “probability”, i.e. what the market thinks the odds are, can swing wildly in the final moments. Even very small price moves or random blips in trading can cause huge changes in the price of the binary option.

For traders, this creates two big problems: timing risk and cost drag. If you click “buy” just a few seconds too early or too late, the price you get can be very different, even if nothing meaningful changed in the real world. You still pay the same transaction costs (spread and fees), but your odds of actually profiting can be lower because of this hypersensitivity.

Market design and incentive alignment

In many retail venues, the platform or its affiliated market maker is the principal to client trades. Revenue scales with turnover, spreads, early-exit costs, and, in some jurisdictions, with net client losses. This creates a measurable incentive to maximize trading frequency and maintain short clocks.

Platform choices that increase expected platform revenue also increase expected customer loss:

1. Short maturities
   High gamma and noise dominance inflate Δ and rejection rates at displayed prices, boosting effective costs per decision.
2. At-the-money framing
   Most contracts are listed near 50 “probability,” which maximizes variance of outcomes and encourages repeated re-entry after losses.
3. Early-exit asymmetry
   Buybacks are quoted at unfavorable implied probabilities, embedding another wedge beyond the entry spread.
4. Deposit and bonus turnover conditions Withdrawal frictions tied to notional volume prolong exposure and raise the likelihood of ruin for equal-edge players.

From a mechanism-design perspective, this is a negative-sum repeated game for the median retail participant once frictions are included.

Cost decomposition and break-even skill

Let Δ denote half-spread (in probability points), c explicit fees per contract (in payout units), and p^* the trader’s true event probability. The minimum forecast advantage ε over the venue’s implied probability p required to break even satisfies

ε ≡ ( p^* − p ) ≥ Δ + c.

With typical retail spreads of 1–4 points and non-zero fees, ε must be several percentage points, every trade, net of selection and timing error. Empirically, sustained ε at that level is rare for individuals without privileged data, especially at sub-hour horizons where variance swamps signal.

Example

Imagine you’re trading on a prediction market — like betting on whether something will happen (say, “Will it rain tomorrow?”). The market´s implied probability for the event says there’s a 60% chance of rain. You have your own estimate and you think there’s a 65% chance of rain.

You might want to bet on it because you think the market is wrong in its implied probability, but before you can make money, you have to overcome both spread and fees. The spread is the built-in difference between buying and selling prices. The platform can also charge various fees, e.g. a small commission per trade.

So, for your bet to even break even, your advantage (your forecast being more accurate than the market’s) must be big enough to cover both the spread and any fees. Even if you’re a little better than average, that’s often not enough to profit once spreads and fees have been deducted form the profit. Since spreads and fees eat into your edge, you need to be several percentage points more accurate than the market each time. In practice, very few people can consistently do that without insider information or very sophisticated models, especially over short timescales when luck and random noise dominate.

Path dependence near expiry and settlement ambiguity

Settlement commonly references a platform-chosen feed and a specific timestamp. Around the decision time, order queues, throttling, and quote refresh intervals create discrete-time sampling of a continuous-time process, making outcomes sensitive to micro-latency and to the exact tick used for settlement. Small discrepancies between public charts and the platform´s benchmark are immaterial for linear payoffs but decisive for binary payoffs. Without independent tick archives, disputing these boundary cases is difficult, which further loads the coin against the trader.

Behavioral reinforcement and loss escalation

Variable-ratio reinforcement schedules (wins and losses at irregular intervals) increase response persistence. Combined with short feedback loops, this induces classic escalation patterns in many traders: post-loss risk seeking and martingale-style bet sizing. In a binary-payoff environment, martingale schemes convert a negative-drift process with frequent small losses into a process with long plateaus and catastrophic drawdowns. Gambler’s ruin probabilities rise rapidly when the loss distribution is heavy-tailed and capital buffers are thin, which is the typical retail context.

Volatility clustering and regime sensitivity

Returns exhibit volatility clustering and jumps. For digital payoffs, a jump process near maturity dramatically increases the variance of N(d₂), widening practical spreads (displayed or implicit) exactly when many participants are most active.

Platforms benefit via increased turnover and slippage, as traders face higher effective costs at the same stake size. Any backtest that assumes iid noise or constant σ will overstate attainable edge net of frictions.

In other words, markets tend to move in bursts and binary options are very sensitive near the finish line.

The price of the underlying asset is not likely to drift up and down evenly. Prices often move in clusters of volatility, where quiet periods are followed by sudden bursts of activity. Prices can also jump sharply due to news, rumors, or liquidity shocks. When you get close to expiration for “yes/no” bets like binary options, even a tiny price jump can completely change the outcome from win to loss, or vice versa.

So if volatility or jumpiness increases near the end, the market’s quoted odds for that binary can start swinging wildly. The market-maker knows this and usually widens the spread (the gap between buy and sell prices) to protect themselves from the uncertainty. Execution quality can also get worse when most traders are active. So, you might think you’re trading “cheaply” (same nominal stake), but in reality you’re paying more through slippage (getting worse prices) and hidden costs (wider effective spreads).

If you test a trading strategy using historical data but assume price changes are nice and smooth (independent, constant volatility), you’re missing the real-world effects of volatility bursts and jumps. In the real market, those bursts make execution worse, spreads wider, and slippage bigger, so your actual profits would be much lower than the backtest suggests.

Real markets tend to move in jerky bursts. Binary options amplify that jumpiness near expiration, making prices and spreads unstable exactly when you’re trying to trade. Platforms make more from that extra activity, but traders end up paying higher costs. Any strategy that assumes calm, regular price movement will look better on paper than it performs in the wild.

Comparison with vanilla options and linear instruments

A vanilla call option aligns payoff with move size and permits continuous risk management (delta hedging in theory; partial exits in practice). A linear position (cash equity, futures contract, or CFD) maps P&L to signed distance, again allowing partial de-risking. The binary option´s fixed payoff removes that gradient, so there is no “soft landing” for ideas that are directionally correct but mistimed by minutes. Consequently, the expected shortfall conditional on being wrong is larger for binary options than for vanilla option structures at comparable notionals.

Why the binary option tends to be loss-making in retail use

Putting the parts together:

1. Negative edge by construction
   There is a −(Δ+c) expectancy per trade unless the trader’s probability forecasts exceed the market’s by at least Δ+c.
2. Edge erosion by micro structure
   Last-tick sensitivity, rejection slippage, and settlement opacity reduce realized edge relative to modeled edge.
3. Behavioral amplification Short clocks combined with fixed payoffs make traders more likely to engage in over trading and go for adverse sizing after losses, raising realized costs.
4. Incentive conflicts Principal dealing and turnover-linked revenue bias design toward high-frequency, high-variance decisions that favor the house.

Under these conditions, even fairly decent forecasting skills will be insufficient to produce durable positive expectancy for most participants.

Practical implications for risk management and policy

For individuals, the scientifically consistent stance is staying away from binary options, or use them with extreme caution and solid risk-management rules in place. Avoid ultra-short expiries, avoid martingale sizing, and recognize that achieving the break-even ε persistently is statistically unlikely without superior information and tooling.

For supervisors, such as financial authorities, instituting and enforcing mandatory transparency around binary options benchmark feeds, archived ticks, explicit wedges by time bucket, and withdrawal rules would reduce information asymmetry between trader and platform. From a consumer welfare lens, steering inexperienced users toward instruments with graduated payoffs and controllable exits aligns better with long-term capital formation.

Summary

A retail binary option trade is a Bernoulli trial with success probability p^*, payoff +1 on success and −B on failure, executed at a price B = p + Δ with fee c. Under mild assumptions p^* ≈ p for the median participant, the expected return per trial is −(Δ+c).

Short-horizon variance, execution frictions, and behavioral responses further decrease the sample mean relative to this theoretical expectation. Therefore, absent persistent superior calibration exceeding transaction wedges, the product is designed, via both payoff structure and market microstructure, to yield negative expected returns for typical retail users.