Compiling and forecasting implied volatility surfaces via survey sampling, tempered inverse-probability sequence learning, and causal activity clocks

Abstract

Compiling implied volatility (IV) surfaces and forecasting derivative risk from high-frequency equity and options feeds requires addressing contract heterogeneity, schema shifts, volatility clustering, and non-stationary trading activity. Using a split-adjusted NVIDIA (NVDA) equity and options panel (2018-2025), this study integrates finite-population survey sampling, tempered inverse-probability sequence learning, and causal activity clocks. Four findings emerge. First, cross-sectional surface accuracy depends on matching the sampling design to the target functional: plug-in stratified allocations using lagged cell dispersion improve equal-weighted surface reconstruction with full grid coverage, whereas liquidity-weighted probability proportional to size (PPS) sampling excels on liquidity-weighted targets by construction yet inflates error when misapplied. Second, in longitudinal LSTM sequence training, PPS and Neyman designs retain more tail-volatility windows than simple random sampling (SRS); all three designs are equivalent to full-census training within chosen margins while cutting training time, though incremental forecasting gains of informative selection over SRS are not established. Third, out-of-sample evaluation shows a predictability contrast: short-horizon prices are not forecastable beyond a random walk with drift among tested models, whereas forward IV shows descriptive mean-reversion skill concentrated in a few post-shock reversal sessions (insignificant under session-clustered tests), with sequence models not beating a linear HAR-IV benchmark and feature pruning driving stability. Fourth, across a 6.3x start-to-end (nearly twentyfold trough-to-peak) price expansion, rolling volume and dollar clocks stabilize bar rates and compress intraday return kurtosis beyond diurnal scaling.