Paper: arXiv 2610.33438

Authors: Deepak Bastola, Eli Prushansky

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 9.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper demonstrates a high level of mathematical sophistication in integrating various statistical and machine learning techniques. Its empirical rigor is exceptional, with detailed data analysis, robust statistical testing, and clear out-of-sample evaluations. The novelty lies in the unique combination of survey sampling, sequence learning, and activity clocks for volatility forecasting.

Research Flowchart

  flowchart TD
    A[Research Goal: Compile & Forecast Implied Volatility (IV) Surfaces & Derivative Risk] --> B{Key Methodologies};
    B --> C[Data: Split-Adjusted NVDA Equity & Options Panel (2018-2025)];
    B --> D[Methodology: Finite-Population Survey Sampling (Stratified, PPS, SRS)];
    B --> E[Methodology: Tempered Inverse-Probability Sequence Learning (LSTM)];
    B --> F[Methodology: Causal Activity Clocks (Rolling Volume/Dollar Clocks)];
    C & D & E & F --> G[Computational Processes: Surface Reconstruction, LSTM Training, Out-of-Sample Evaluation, Feature Pruning];
    G --> H[Findings: 1. Sampling design impact on surface accuracy; 2. Sampling benefits in LSTM training; 3. Predictability contrast (prices vs. forward IV); 4. Activity clock stabilization.];