Modeling Intraday Volatility Patterns

When To Use

• Constructing volatility curves across the trading day for VWAP/TWAP execution scheduling
• Estimating open-auction and close-auction volatility premiums for order sizing
• Quantifying lunch-time liquidity troughs and their impact on spread and slippage
• Building event-window volatility overlays (e.g., FOMC announcements, earnings releases, index rebalances)
• Calibrating intraday risk limits or dynamic hedging intervals for market-making books

Inputs To Gather

• Tick or bar data: Trade prices and volumes at 1-min (or finer) intervals for the target instrument(s); minimum 60 trading days for stable seasonality estimates
• Session boundaries: Exchange open/close times, auction windows, early-close calendar [VERIFY against exchange-specific schedules]
• Event calendar: Scheduled macro releases (FOMC, NFP, CPI), earnings dates, index rebalance dates, options expiration dates
• Reference volatility: Daily realized volatility (close-to-close or Yang-Zhang) and implied volatility term structure for normalization
• Market structure context: Tick size, lot size, average daily volume, primary vs. consolidated feed [VERIFY for each venue/asset class]

Workflow

1. Clean and align data

   • Remove pre-market / after-hours prints unless explicitly modeling extended sessions
   • Align timestamps to exchange time; handle daylight-saving shifts
   • Filter obvious bad ticks (price > 3× median absolute deviation from rolling median)

2. Compute raw intraday volatility profile

   • Calculate return variance per interval bin (e.g., each 5-min bucket across all sample days)
   • Use Garman-Klass or Parkinson estimators on OHLC bars for efficiency when tick data is sparse
   • Normalize each day's profile by that day's total realized variance to isolate the seasonal shape from the level

3. Estimate the U-shape (or W-shape) seasonal component

   • Average the normalized variance profiles across the sample to extract the deterministic intraday pattern
   • Confirm the characteristic open spike, mid-morning decay, possible lunch trough, and closing ramp
   • Fit a flexible functional form (Fourier series with 3–5 harmonics, or cubic spline with knots at open, 10:00, 12:00, 14:00, close) for smooth interpolation

4. Overlay event-driven adjustments

   • Partition sample days into event vs. non-event subsets
   • Compute the incremental variance ratio at each interval during event windows (e.g., ±30 min around FOMC release)
   • Express event impact as a multiplicative scaling factor on the baseline seasonal curve

5. Validate the model

   • Hold out the most recent 20% of trading days for out-of-sample testing
   • Compare predicted interval variance to realized interval variance; report RMSE and mean absolute percentage error per bucket
   • Check that the model correctly ranks high-vol vs. low-vol intervals at least 80% of the time (concordance test)
   • Stress-test on known anomaly days (flash crashes, circuit-breaker halts) to confirm degradation is bounded

6. Produce outputs and integrate

   • Generate a per-interval volatility multiplier table (baseline + event-adjusted) for use in execution algorithms
   • Derive recommended participation-rate adjustments: increase participation during low-vol intervals, reduce during spikes to limit impact
   • Package as a callable function or lookup table consumable by the OMS/EMS

Output

• Intraday volatility curve: Normalized variance (or standard deviation) by interval, with confidence bands
• Event overlay table: Multiplicative volatility scalars keyed by event type and time-offset from release
• Execution timing recommendations: Suggested participation-rate schedule or optimal slice boundaries for VWAP/IS algos
• Model diagnostics: Out-of-sample fit statistics, residual autocorrelation plots, day-type breakdown (Monday effect, triple-witching, etc.)
• Assumptions log: Data window, estimator choice, outlier-filter parameters, event classification rules

Quality Checks

• Confirm the seasonal curve integrates to 1.0 (variance shares must sum to total daily variance)
• Verify open and close buckets show statistically significant elevation vs. midday (t-test or bootstrap)
• Ensure event scaling factors are estimated on ≥ 15 event instances to avoid small-sample bias [VERIFY for less-frequent events like Fed emergency meetings]
• Cross-check volatility levels against implied volatility for the same tenor; flag divergences > 2 vol points
• Validate that lunch-trough depth is consistent with observed spread widening in the underlying market data
• Mark any asset-class-specific assumptions (e.g., equity vs. futures session times, FX 24-hour cycle) with [VERIFY]