The Shrinking Edge

A Polymarket contract that pays $1 if Bitcoin is above a strike at noon is a digital option. Below, a textbook formula prices one real contract at every one of its 6,998 fills, from public spot data alone. Scrub through the last 36 hours, bend the formula's volatility, and watch where it agrees with the market, where it disagrees, and what following it would have cost.

Companion page to takakhoo/prediction-market-research-agent. Every number here is computed in your browser from the committed sample and result tables. Nothing on this page is investment advice.

1. One contract, fill by fill

Binance spotstrikePolymarket fillsoption model valuefills the rule takes

time volatility x 1.00 rule bar 10 cents

Inputs the formula sees at the cursor: the last one-minute candle that had closed, the time to the settlement candle named in the contract's rules, and realized volatility over a trailing window about four times the horizon. Nothing is fitted. The volatility slider multiplies that trailing estimate so you can see how much the verdict depends on it. The fill at the cursor is the real one; the tally counts every earlier fill the rule would have taken at the current settings and what those fills made when the contract settled.

2. The formula

value of Yes = Φ(d₂), d₂ = ( ln(S / K) − σ²τ / 2 ) / ( σ √τ )

S is spot, K the strike, τ the time to settlement in years, σ annualized volatility, and Φ the standard normal distribution function. The rule takes a fill when the side the taker bought is worth at least the bar more than its price plus the fee, where the fee is rate × price × (1 − price) per share.

spot 100.0 strike 103.0 hours left 24 volatility 60% a year

value of Yes

value of No

fee at that price, rate 0.07

The curve is the value of Yes against spot at the chosen volatility and horizon. It sharpens into a step as expiry approaches.

3. The same rule under each successive control

Score the rule at displayed prices and it looks like free money. Score it at prices that traded, with older information, limited capital, fees, and in a confirmation period chosen in advance, and most of it is gone. Hover a row for the interval.

By the age of the spot data the formula sees

By settlement quarter

4. Where the money went

Cumulative profit of the capped replay (15-minute-old spot, $200 per fill, profit booked at expiry). The shaded region is the confirmation period, April to September 2026, after the rule's threshold was fixed on earlier contracts.

Source, data, paper, and the full audit: the repository.