Development of AI Volatility Forecasting Model
Volatility forecasting — key task for options trading, risk management and position sizing. Unlike price forecasting (nearly impossible), volatility clusters and is predictable: high volatility today predicts high volatility tomorrow.
Types of Volatility
Historical Volatility (HV): realized volatility for past period. Simplest calculation: standard deviation of log returns × √252 (annualized). Depends on chosen window: 10d, 21d, 63d give different values.
Implied Volatility (IV): market's assessment of future volatility, "embedded" in option prices (inverse Black-Scholes problem). VIX — 30-day implied volatility for S&P500.
Realized Volatility (RV): high-frequency estimate of true volatility. Computed from intraday returns: RV = √(Σ r_i²). More accurate than standard HV.
GARCH and Extensions
GARCH(1,1) — Basic Statistical Approach:
σ²_t = ω + α × ε²_{t-1} + β × σ²_{t-1}
Parameters: ω (baseline volatility), α (shock persistence), β (variance persistence). Sum α+β close to 1 = persistence effect.
Extensions:
- GJR-GARCH / EGARCH: asymmetry (leverage effect — declines increase volatility more than rises)
- GARCH-DCC: Dynamic Conditional Correlation — correlation matrix for portfolio
- HAR-RV (Heterogeneous Autoregressive RV): uses daily, weekly and monthly RV as predictors
ML Volatility Models
Feature Set:
features = {
'rv_1d': realized_volatility(returns, '1D'),
'rv_5d': realized_volatility(returns, '5D'),
'rv_22d': realized_volatility(returns, '22D'),
'iv_atm': implied_volatility_atm, # if available
'iv_skew': iv_25d_put - iv_25d_call,
'vix': vix_level,
'vvix': vvix, # volatility of VIX
'volume_ratio': volume / sma_volume_20d,
'return_1d': log_return_1d,
'abs_return_5d': abs(log_return_5d)
}
Neural Network Models:
- LSTM with RV features: well captures volatility clustering
- WaveNet: dilated causal convolutions for long contexts
- Transformer: allows attention on different time horizons
Comparative Result (MSE on 1-day forecast): HAR-RV → GARCH → LightGBM → LSTM ≈ Transformer. Difference between best ML and HAR-RV: 5-15% on MSE. HAR-RV surprisingly strong baseline.
Volatility Surface Forecasting
For options desk, need forecast not of single point, but volatility surface (IV across all strikes and expiries):
Parametric Models:
- SVI (Stochastic Volatility Inspired) parameterization: 5 parameters per slice
- SSVI (Surface SVI): adds no-arbitrage constraints
ML for Surface Dynamics:
- PCA on historical surfaces → predict PC coefficients → reconstruct surface
- Autoencoder + temporal model (LSTM): encode surface, predict in latent space
Applying Volatility Forecasts
Options Trading:
- IV > predicted RV → options expensive → short vega strategies (short straddle)
- IV < predicted RV → options cheap → long vega (buy gamma)
- Volatility premium: IV averages 10-30% higher than RV — this is VRP (Volatility Risk Premium)
Position Sizing:
Position_Size = Risk_Budget / (ATR_multiplier × Forecast_Volatility)
With high predicted volatility — smaller position. This is Kelly Criterion in action.
Risk Management:
- VaR (Value at Risk): depends on volatility, updates dynamically
- CVaR / Expected Shortfall: regulatory requirement Basel III
- Margin requirements: for futures/options — dynamic collateral calculation
Production System
Stack:
- QuantLib / py_vollib for theoretical calculations
- Polygon.io / CBOE for IV data
- ClickHouse for high-frequency RV data storage
- Airflow for daily forecast recalculation
Monitoring: Mincer-Zarnowitz regression to assess calibration: predicted volatility should be unbiased predictor of realized. Bias correction on systematic deviation.
Timeline: HAR-RV baseline + GARCH comparison — 2-3 weeks. ML model with volatility surface and trading system integration — 8-12 weeks.