Fair Value Pricing in Short Dated Bitcoin Binary Markets: A Single Window Evaluation of a Candidate Statistical Arbitrage Edge

Abstract

Short dated Bitcoin binary contracts settle over horizons brief enough that expected drift is negligible, which reduces their fair value to a function of current spot and short horizon volatility alone. This paper frames the contract as a cash or nothing digital option, derives a driftless fair value, and defines an entry rule that acts when the implied price and fair value differ by at least a fixed buffer, sizing by a model edge score. On 182 resolved contracts traded across 22 to 23 June 2026, the rule realised a positive statistical edge, a win rate of 67.6 percent against the 63 percent break even rate implied by the mean entry price of 0.63, an edge of 4.6 percentage points. The point estimates are positive across the headline measures, but the sample is too small to establish significance: bootstrap intervals on the edge include zero, and the model fair value does not improve on the market price as a probability forecast. The realised gain is concentrated in a small number of trades and coincides with a directional position, and an edge threshold selection rule does not persist out of sample. The result is interpreted as a statistical edge documented within a single window, whose significance and source, a genuine pricing signal against the established favorite longshot bias, remain open questions pending a larger sample. The contribution is the pricing framework and its evaluation.