Bridge Latency as a Trading Risk Factor: Quantifying Cross-Chain Arbitrage Window Decay

Abstract Cross-chain arbitrage looks attractive on paper: an asset trades at different prices on two chains, you buy cheap on one, bridge it, sell dear on the other. The catch is that the bridge takes time — anywhere from seconds (optimistic liquidity bridges) to tens of minutes (lock-and-mint legacy bridges) — and during that window the price gap moves. This note derives a closed-form model for how the expected arbitrage gap decays as a function of bridge latency, validates it against a Monte Carlo simulation (match within 0.8%), and extracts a single transferable formula for the break-even latency above which a cross-chain arbitrage is no longer profitable in expectation: . For representative parameters the break-even latency ranges from 13 seconds (routine 0.1% spreads) to 2.5 minutes (large 1% event-driven gaps), which is shorter than almost every production bridge. The implication is stark: most bridge-mediated cross-chain arbitrage is structurally negative-EV at observed gap magnitudes, and the viable strategies are either (a) atomic hedging on the source chain with no bridge wait, or (b) waiting for genuinely large dislocations. Hypotheses - H1 (high confidence): The expected captured arbitrage gap decays exponentially with bridge latency, , under a mean-reverting gap process. Validated by Monte Carlo to within 0.8% of . - H2 (high confidence): The break-even latency scales logarithmically with the gap-to-cost ratio, . Doubling the gap extends the viable window by only seconds at representative . - H3 (medium confidence): For latencies beyond a few half-lives, the probability of profitability converges to a constant plateau that is independent of the initial gap. At benchmark parameters this plateau is 0.159 — meaning even with infinite patience you profit on fewer than 1 in 6 attempts. Data Provenance | Input | Value | Provenance | Reliability | |-------|-------|-----------|-------------| | Gap mean-reversion | 1.0 /min | Calibrated to cross-exchange spread half-life; literature on DEX arb decay (UNRELIABLE — single point estimate) | UNRELIABLE | | Stationary gap std | 0.08% | Set to match long-run spread dispersion in our CEX monitoring | RELIABLE | | Initial gap | 0.10% / 1.00% | Lower bound from our observed cross-venue spreads (AXL: 0.21%, FIDA: 0.12%); upper bound = event scenario | RELIABLE | | Round-trip cost | 0.08% | Bridge fee + destination gas + source gas + slippage, public fee schedules (UNRELIABLE — varies by bridge and chain) | UNRELIABLE | | Monte Carlo paths | 300,000 | Exact OU discretization, numpy PRNG seed 20260701 | RELIABLE | | Closed-form formulas | — | Derived analytically; cross-checked against simulation | RELIABLE | Our operational context: the PerpsTrader spread monitor records persistent cross-venue gaps of 0.02%–0.21% between AsterDEX and Binance (e.g. AXL 0.21%, FIDA 0.12%, PORTAL 0.10%, CHZ 0.07%). These gaps are the empirical motivation for the model. They are not measurements of the gap process — they are point-in-time observations used only to set . The process parameters () are model assumptions, not fitted estimates. The Model Why the gap mean-reverts When an asset trades at on chain A and on chain B with , the gap attracts arbitrageurs. Each execution buys A and sells B, mechanically compressing the gap. In a competitive market the gap therefore reverts toward zero. The canonical model for a mean-reverting quantity is the Ornstein-Uhlenbeck (OU) process: $\kappa 0\sigma\sigma{\mathrm{eq}}^2 = \sigma^2/(2\kappa)\taug0\tau\tau{1/2} = \ln(2)/\kappa\mathbb{E}[g(\tau)] = cc\tau^g(\tau)\tau \to \inftye^{-\kappa\tau}\to 0\sigma{\mathrm{eq}}^2c = \sigma{\mathrm{eq}} = 0.08\%1 - \Phi(1) = 0.159g0g0g0g0\tau^\kappag0/c\kappag0/c\kappa=0.3\kappa=5g0/c = 10\times\taug0g0\mathbb{E}[g(\tau)]\tau^\tau^ = \kappa^{-1}\ln(g0/c)\kappag0c\Pr\infty = 1-\Phi(c/\sigma{\mathrm{eq}})1/\kappa\kappa=0.3\kappag0/c \gg 1\kappa\kappa=1.0c\kappa\sigma{\mathrm{eq}}cg0\tau^ = \kappa^{-1}\ln(g0/c)\tau^\kappa$. 5. Venym Labs internal data: cross-exchange spread monitor, PerpsTrader databases (944,150 funding observations; AsterDEX↔Binance spread snapshots). Provenance: SIMULATED/OPERATIONAL — point-in-time observations, not process estimates.