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Summary

Before any machine-learning vol model is entertained, the system must hold fixed, well-understood baselines: simple realized-volatility estimators, GARCH-family conditional-variance models, and the HAR-RV regression on realized volatility. The EV contract in source.md requires every playbook to report a GARCH/HAR-class forecast as its baseline comparator; positive EV without beating that baseline is not edge.

Realized-Volatility Estimators

Estimators of historical (realized) volatility differ in how they use the day's price path. With only daily bars, the classic estimators are available; with intraday data (ThetaData 1-min bars from 2016) one can compute true high-frequency realized volatility.

Estimator Inputs Notes
Close-to-close daily closes Standard deviation of log returns over a rolling window; ignores path; noisy
Parkinson daily high, low Uses intraday range; roughly 5× more efficient than close-close under a driftless diffusion
Garman–Klass OHLC per day Combines open/close with high/low; ~7.4× more efficient, but biased by gaps and microstructure noise
Rogers–Satchell OHLC Handles nonzero drift
Realized vol (RV) intraday returns Sum of squared intraday returns; the empirical foundation of HAR-RV

The books treat historical vol as the raw input to IV comparison: Natenberg builds forecasting intuition from statistical vol and its mean reversion[^natenberg-vol], and Chen & Sebastian stress that IV mean reverts toward its own history — the spread IV − RV (the variance risk premium) is the trading signal, not the forecast alone[^tohf-vol].

GARCH Family

GARCH(1,1) models conditional variance with persistence: σ²ₙ = ω + α·u²ₙ₋₁ + β·σ²ₙ₋₁, with a long-run variance level implied by the parameters. Hull's fitting of S&P 500 daily data (α ≈ 0.083, β ≈ 0.910, long-run vol ≈ 1.44%/day) and the RiskMetrics EWMA special case (λ = 0.94) are the canonical examples[^hull-var]. Key properties:

  • Strong, robust capture of volatility clustering — the dominant empirical fact of daily returns.
  • Naturally produces multi-horizon forecasts with mean reversion toward the long-run level, which can be compared against the IV term structure[^hull-smiles].
  • Extensions (EGARCH, GJR-GARCH) add asymmetry: negative returns raise future vol more than positive ones, matching the leverage effect.
  • Cheap, few parameters, hard to beat consistently out-of-sample.

HAR-RV

The Heterogeneous Autoregressive model of Corsi (2009) regresses future realized volatility (typically over 1-day, 1-week, 1-month horizons) on lagged RV at daily, weekly, and monthly frequencies, capturing the superposition of trader heterogeneity. Strengths:

  • Uses high-frequency RV directly, so it exploits more information than daily-only GARCH.
  • Ordinary least squares — no likelihood optimization, stable, transparent.
  • Empirically at least as accurate as GARCH for RV forecasting in the academic literature; it is the standard yardstick in the realized-vol forecasting literature.

Why ML Must Beat the Baseline

Volatility is close to its own history, highly persistent, and mean-reverting; these facts are captured almost fully by GARCH and HAR. Consequences for the ML program:

  1. Any proposed model (ridge, forests, GBMs, sequence models — see ml-for-vol-prediction.md) must show out-of-sample improvement over GARCH(1,1) and HAR-RV on the same evaluation windows, not in-sample fit statistics.
  2. Small apparent gains are often artifacts of lookahead, overlapping forecast horizons, or a single regime (see backtest-discipline.md).
  3. The actionable quantity is usually the spread — forecast vol versus IV, i.e. the variance risk premium — so a forecast that is slightly better in RMSE but uncorrelated with tradable IV mispricing adds nothing.

Typical Horizons

Horizon Primary use Baseline of choice
1 day delta-hedging, 0DTE sizing GARCH/EWMA, HAR (daily RV)
1 week weekly short-vol structures HAR-RV
1 month (20–30d) monthly premium selling, calendar pricing HAR-RV, GARCH term forecast vs IV term
3+ months structural positioning, regime framing Long-run mean reversion, regime models

These horizons align with the regime context required by the EV contract; regime conditioning lives in 60-regimes/index.md.

References

  • Tim Bollerslev, "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics 31 (1986).
  • Franco Corsi, "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics 7(2), 2009.
  • M. Garman & M. Klass, "On the Estimation of Security Price Volatilities from Historical Data," Journal of Business 53(1), 1980.
  • O. E. Barndorff-Nielsen & N. Shephard, "Econometric Analysis of Realized Volatility," Econometrica 72(3), 2004.
  • John Hull, Options, Futures and Other Derivatives, 8th ed., Chapter 22 (EWMA/GARCH).
  • Sheldon Natenberg, Option Volatility and Pricing, chapters on historical volatility forecasting.

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