How Fast Do Prices Reach a Target? Volatility Scaling of First-Passage Times, the Overnight Gap, and a Censoring Bias in Its Measurement

The time a price needs to move by a given percentage is a basic input to trading rules, risk limits and holding-period design. Under diffusion, the median time to a first touch of a symmetric barrier ±X scales with the inverse square of volatility relative to the barrier. We measure this relation on 15-minute bars of 17 instruments from five asset classes (equity, bond, commodity and currency ETFs, and three crypto-assets) and report three findings. First, the scaling exponent is far from the diffusion value of −2 and varies widely, from −1.50 to +0.03. Second, the variation is not an asset-class property: a single microstructure variable, the share of first touches that occur on the first bar of a trading session, explains 68% of the cross-sectional variance on its own and 72% together with a discretisation term; a joint monthly block bootstrap places the gap coefficient well away from zero. When the overnight channel is removed by measuring within sessions only, equity and bond ETFs return to −1.96 and −1.84, close to diffusion. Continuously traded crypto-assets show no gap channel and settle at −1.3 to −1.5, which we attribute to jumps and heavy tails. Third, the exponent is sensitive to right-censoring: a short observation horizon combined with a median over touched observations only flattens the estimate by up to 0.46. We propose a three-regime reading of the law (diffusion, gap-dominated, discretisation floor), a censoring-consistent estimator, and practical rules for porting time-based exits across instruments.

This record contains the English original and a German translation („Wie schnell erreichen Preise ein Kursziel?“).