Uniform one-sided conformal bands for forward realized volatility curves

We introduce uniform, one-sided conformal prediction bands for forward realized volatility (FRV) paths that control the entire trajectory up to a fixed horizon $ H $ with finite-sample, distribution-free marginal validity. The construction is model-agnostic: A monotone (isotonic) baseline across horizons and robust per-horizon scales are fitted to the training data; a scaled sup-norm score calibrated on a chronological holdout yields the uniform envelope. To address serial dependence, we employ block-maxima calibration; for regime sensitivity, we add group conditional (Mondrian) variants based on training-only state variables. On eight liquid assets, the method achieves conservative uniform coverage while adapting the width to tail risk: Bands are widest for crypto and oil, and tightest for broad equities and treasuries. A simple operational law emerges, namely that the mean one-sided width grows approximately with $ \sqrt{H} $, turning the horizon design into a transparent safety-tightness trade-off. Practical guidance is given as follows: $ \alpha\!\approx\!0.05 $ is a reliable default for thinner tails, while $ \alpha\!\in[0.05, 0.025] $ increases safety where bursts are frequent. Relative to parametric benchmarks such as heterogeneous autoregressive realized volatility (HAR-RV) and generalized autoregressive conditional heteroskedasticity (GARCH) models, our bands remain valid across regimes and stay width competitive in calmer markets. The algorithm is linear in $ nH $ and agrees with deployment diagnostics. Overall, uniform FRV envelopes provide an operationally transparent, model-agnostic tool for pathwise volatility control, with tunable conservatism and simple extensions for dependence, covariate shift, and cross-split stability.