@article{Sözen2025, 
author = {Çağlar Sözen},
title = {Uniform one-sided conformal bands for forward realized volatility curves},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {27314-27337},
keywords = {conformal prediction, forward realized volatility (FRV), uniform upper bands, isotonic regression, robust scaling, block-maxima calibration, Mondrian calibration, risk management},
url = {https://www.sciopen.com/article/10.3934/math.20251201},
doi = {10.3934/math.20251201},
abstract = {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        H  , turning the horizon design into a transparent safety-tightness trade-off. Practical guidance is given as follows:    α    ≈    0.05 is a reliable default for thinner tails, while    α    ∈  [  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    n  H 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.}
}