Theta Edge

What Options Traders Know That Prediction Markets Don't

On any professional options desk, a 65¢ binary contract expiring in 2 hours and a 65¢ binary expiring in 2 weeks are two completely different products. They have different deltas, different gammas, different thetas. The price that accounts for all of that is not 65¢ in both cases. But on Polymarket and Kalshi, the crowd treats them identically. The market prices probability. It does not price time.

That gap is the theta edge. The binary options model says: given a current probability p and time remaining τ, with a calibrated daily volatility σ, what would a properly-priced binary option cost? The answer is almost never equal to the raw market price when there is meaningful time remaining. Either the contract should be worth more (BUY) or less (SELL) than what the crowd has priced.

The Model

The Theta Edge calculator models the log-odds of the probability — logit(p) = ln(p / (1 − p)) — as a Brownian motion with daily volatility σ. At resolution (τ = 0), the price collapses to 0 or 1. The fair value at any time τ is the probability that the random walk, starting at logit(p), is still positive at expiry:

FV = Φ( logit(p) / (σ × √τ) )

The σ parameter is the key calibration. An active political market — the type where a contract at 82¢ with 14 days left should price at 72¢ — implies a daily log-odds volatility of approximately 0.70. At p = 0.5, that is about 17 probability points per day of movement. Stable markets use lower σ; crypto and breaking-news markets use higher.

BUY vs. SELL

A BUY signal means the market price is below the binary fair value. This happens most often with high-probability contracts that still have significant time remaining — the crowd has not pushed the price up to where the binary model says it belongs given the remaining time for probability to converge.

A SELL signal means the market is overpricing certainty. The crowd has pushed a high-probability contract to 80¢+ when the binary model — accounting for σ days of remaining volatility — says it is only worth 72¢. The excess is the favourite-longshot bias in reverse: people see a likely outcome and price it as more certain than the remaining time justifies.

The Decay Curve

The time decay curve shows how the binary fair value changes as the contract approaches expiry. For in-the-money contracts (above 50¢), the fair value rises toward 100¢ as expiry approaches — positive theta. For out-of-the-money contracts, fair value falls toward 0¢. The market price is shown as a horizontal reference line. The gap between the two lines is the edge available at any time horizon.