Delayed Marks, Funding Memory, and Forecasting Liquidation-Tail Risk in Crypto Perpetual Futures

Abstract

Crypto perpetual futures embed liquidation risk in one chain: leverage and funding move the margin boundary, the mark determines when a crossing is observed, and executable depth determines the concession paid after detection. The primary forecasting question is how to quantify both the probability of an isolated-margin boundary breach and the loss hidden by delayed or smoothed detection. This paper develops a first-passage density-forecasting framework in which the executable price is observed through a delayed or smoothed mark, funding is a persistent collateral drain, and liquidation occurs when isolated-margin surplus reaches its maintenance boundary. The output is a joint predictive distribution: a horizon-specific probability of a boundary breach and, conditional on detection, a distribution of catch-up loss. Under a fixed delay, expected overshoot is σδ/2π, and bad-debt probability is a Gaussian tail governed by the latency-to-margin ratio σδ/m. Its leverage independence is exact only in the constant-maintenance, fixed-non-price-drain benchmark. For time-weighted-average marks, fixed-time variance reduction does not imply liquidation-time safety. A stationary-downcrossing approximation size-biases the stale error in the adverse direction, producing a mean overshoot about 1.6 times the same-window fixed-delay value. A rolling comparison with historical simulation scores model-consistent margin-breach forecasts from public price and funding paths. The structural forecast has lower Brier scores at 10× over 24-, 72- and 168-hour horizons and across the 24-hour grid, but historical simulation performs better for one-week forecasts at 20× and 50×. The evidence supports a conditional risk-forecasting use of the framework, while not establishing uniform forecast dominance.