Optimal Mean-Reversion Pairs Trading in Cryptocurrency Markets: A Limits-of-Arbitrage Study

Abstract

We implement the Leung-Li optimal double-stopping framework for Ornstein-Uhlenbeck spreads and apply it to all 4,950 pairs of the top-100 USD-quoted symbols on Kraken spot at one-minute resolution (Dec 2024 - Dec 2025; 38,241 simulated round trips). To make the framework computable at scale we start from the classical representation of the fundamental solutions F and G as parabolic cylinder functions and derive log-derivative ratio forms that cancel an exp(beta^2/4) overflow factor, enabling vectorized root-finding for the optimal entry and exit levels. The empirical result is a sharp negative: mean reversion is real (gross $2,414; net +$1,896 at the 2 bps design fee, 81% win rate) but the gross edge is an illiquidity premium, rising monotonically from -$4 among liquid majors to +$1,823 in the illiquid tail (75.5% of the total), exactly where spreads, borrow, and ~$14k capacity make it unharvestable. At the realistically attainable 0.24% taker fee every liquidity bucket is negative and the book loses $1,496. Four salvage attempts (cheaper venue, cross-exchange basis, ML meta-labeling, cost-aware bands) all fail; the ML filter posts a deflated Sharpe of exactly zero. We document three methodological errors that disguised the result and read the finding through Shleifer-Vishny limits of arbitrage: the inefficiency persists because harvesting it costs more than it pays.