Volatility Forecasting: From GARCH to Deep Learning — Wiki | SOPHIE

Overview

Volatility, unlike price, is latent — it must be estimated, not observed directly. Forecasting it even 1-2% more accurately than competitors is worth billions to elite options market makers. The field's evolution runs from interpretable econometric models (GARCH) through tree-based ensembles to deep learning architectures, each trading interpretability and speed for predictive power.

Key Concepts

Volatility's stylized facts — clustering (high-vol periods follow high-vol periods), mean reversion (extreme spikes are usually temporary), fat tails (extreme moves are more common than a normal distribution predicts), and the leverage effect (negative price shocks increase volatility more than equivalent positive shocks).
Realized vs. Implied Volatility — Realized Volatility (RV) is backward-looking, computed from historical price data. Implied Volatility (IV) is forward-looking, extracted from option prices. The spread between an RV forecast and current IV is a primary source of volatility-arbitrage alpha.
GARCH(1,1) — the workhorse volatility model: σ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁. ω is the long-run baseline variance, α measures reaction to yesterday's shock, β measures persistence of yesterday's volatility. For most financial assets, α + β ≈ 0.95-0.99 (very high persistence).
Asymmetric extensions — standard GARCH treats positive and negative shocks symmetrically. GJR-GARCH adds a leverage term (γ) that activates only for negative shocks; EGARCH models log-variance directly, guaranteeing positivity while separately capturing shock magnitude and sign effects.

The Machine Learning Frontier

Model Class	Typical R²	Character
GARCH family	~0.15-0.25	Fast, interpretable
Tree ensembles (XGBoost, RF)	~0.30-0.45	Captures non-linear interactions
Deep learning (LSTM, Transformer)	~0.35-0.55	Captures sequential/long-range patterns

Feature engineering matters more than model choice — technical (vol moving averages, Bollinger widths), market microstructure (bid-ask spread volatility, order book imbalance), alternative data (sentiment, news, search trends), and macro data (rate changes, policy uncertainty) all feed model performance.
Hybrid GARCH+ML models — a two-stage approach: fit GARCH first to capture basic clustering, then train an ML model on the standardized residuals to capture the non-linear patterns GARCH misses. Combines econometric interpretability with ML flexibility.

Beyond GARCH: Stochastic Volatility

The Heston model (1993) treats volatility itself as following a stochastic process (mean-reverting, with its own "vol-of-vol" parameter), correlated with the asset price process via a typically negative correlation (~-0.7 for equity indices) that captures the leverage effect directly. It remains the gold standard for option pricing.

Deployment in Trading

Volatility arbitrage — when the RV forecast exceeds current IV, buy straddles/strangles (long volatility); when RV forecast is below IV, sell straddles/strangles (short volatility), delta-hedging continuously to isolate the pure volatility P&L.
Risk management — volatility forecasts feed directly into Value-at-Risk and Expected Shortfall calculations, portfolio risk budgeting, and stress testing.
Position sizing — sizing positions inversely to expected volatility (as in risk parity or Kelly-criterion approaches) targets a constant risk contribution per position.

Limitations and Failure Modes

Non-stationarity — market structure and participant behavior evolve, causing model decay; no model, however well-fit historically, is exempt.
Black swans — models trained on historical distributions cannot predict events outside those distributions by definition. The 2008 crisis exposed this starkly: VaR models built on normal-distribution assumptions assigned near-zero probability to moves that then occurred, providing false security rather than real risk control.
Correlation breakdown — the 2020 COVID crash saw many volatility models fail as cross-asset correlations spiked toward 1.0, breaking the diversification assumptions models depended on.

Key Takeaways

Volatility forecasting is fundamentally a latent-variable estimation problem, not a simple time-series prediction — this is why realized-vs-implied spread, not raw volatility level, is often the real trading signal.
Model sophistication trades off against interpretability and speed; the right choice depends on the trading horizon (tree models for high-frequency, LSTMs/hybrids for medium-term, transformers for multi-asset).
No volatility model — however sophisticated — is immune to regime shifts and black swans; robust strategies (avoiding excess leverage, stress testing, tail hedging) matter as much as forecast accuracy.
The persistence parameter (α + β in GARCH) directly measures how "sticky" current volatility conditions are expected to be, and is itself a tradable insight.