vol_forecasting

5-day ahead realized volatility forecasting for SPY (2010–2024), with a VRP trading strategy.

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Overview

This project benchmarks a spectrum of volatility models — from classic HAR regressions to a Neural SDE with fractional Brownian motion noise — on the task of forecasting 5-day annualized realized volatility for the S&P 500 ETF (SPY).

All models are evaluated under strict no-look-ahead conditions: features are lagged by at least one day, walk-forward validation uses only past data for each training window, and the test set is always held out chronologically.

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Models

Model	Description
Linear (rolling vols)	OLS on 5d and 20d lagged RV
Linear + VIX	OLS adding VIX as an implied-vol signal
HAR	Heterogeneous Autoregressive model (Corsi 2009): daily + weekly + monthly RV
HAR + VIX	HAR augmented with VIX
Advanced linear	OLS on VIX, 20d RV, VRP, VVIX
LogHAR	HAR in log-vol space with Jensen-correction back to level
ElasticNet (LogHAR)	ElasticNetCV on 8 log-space features + lagged residual AR term
GARCH(1,1)	Classical conditional-variance model (via arch)
Gaussian Process	Matérn(ν=1.5) kernel; date-based split puts COVID in test set for meaningful uncertainty estimates
Random Forest	Walk-forward RF on regime-normalised target (shallow trees, high min_samples_leaf)
Neural SDE (fBm)	Milstein-discretised SDE with fractional BM noise (H ≈ 0.134), conditioned on VIX/VRP features
VolNet	Deep MLP (4 layers, SiLU, LayerNorm) in log-vol space
ShallowVolNet	2-layer MLP in full log-space — neural analogue of LogHAR

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Key findings

• VIX is the single strongest predictor across all horizons (IC peaks at the 5–20d horizon), consistent with the VRP literature.
• Rough volatility: the Hurst exponent of log-RV estimated via R/S analysis is H ≈ 0.13, well below 0.5, confirming the anti-persistent, rough nature of the vol process (Gatheral et al. 2018).
• HAR + VIX is a very strong linear baseline and hard to beat on pure R².
• ElasticNet (LogHAR) improves on plain LogHAR by regularising the 8-feature log-space regression and correcting for residual autocorrelation; the AR term alone without regularisation does not reliably outperform.
• GARCH(1,1) is beaten by the Advanced linear model on MSE; the Diebold-Mariano test confirms this at the 5% level.
• Neural SDE: the fBm-driven SDE with H < 0.5 noise captures the rough clustering of vol better than standard BM; competitive with VolNet in R² with more interpretable dynamics.
• VRP strategy: timing vol-selling by the VRP signal (enter when VRP > 75th expanding percentile) produces a meaningfully higher Sharpe than the always-short benchmark.

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Project structure

vol_forecasting/
├── config.py                  # All hyperparameters in one place
├── main.py                    # End-to-end pipeline
├── requirements.txt
│
├── data/
│   └── loader.py              # yfinance download (SPY, VIX, VVIX)
│
├── features/
│   └── engineering.py         # Feature construction + feature-set registries
│
├── models/
│   ├── baseline.py            # Linear, HAR, LogHAR, ElasticNet
│   ├── garch_model.py         # GARCH(1,1) via arch
│   ├── probabilistic.py       # Gaussian Process + Random Forest
│   ├── neural_sde.py          # Neural SDE with fBm noise
│   └── vol_net.py             # VolNet + ShallowVolNet
│
└── evaluation/
    ├── metrics.py             # Walk-forward R², DM test, IC by horizon, Hurst
    └── strategy.py            # VRP volatility-selling strategy

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Quickstart

pip install -r requirements.txt

# Full run including neural models (~10 min on CPU)
python main.py

# Fast run, skip neural models (~30 sec)
python main.py --no-neural

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Features

All features are lagged by ≥1 day to prevent look-ahead bias.

Feature	Description
rolling_vol_20_lag	20-day realized vol, lagged 1d
rolling_vol_5_lag	5-day realized vol, lagged 1d
abs_return_lag	|r_{t-1}| × √252
vix_lag	VIX / 100, lagged 1d
vvix_lag	VVIX / 100, lagged 1d
vrp	VIX − 20d RV (variance risk premium proxy)
RV_daily/weekly/monthly	HAR components (1d, 5d, 22d lagged RV)
vol_5_ratio	5d RV / 20d RV (regime indicator)
log_RV_*	Log-transformed HAR components
log_vix, log_vvix	Log implied vol
momentum_1w	5-day cumulative log return, lagged
log_volume_diff	First difference of log(volume), lagged

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References

• Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics.
• Gatheral, J., Jaisson, T., & Rosenbaum, M. (2018). Volatility is Rough. Quantitative Finance.
• Bollerslev, T., Tauchen, G., & Zhou, H. (2009). Expected Stock Returns and Variance Risk Premia. Review of Financial Studies.
• Diebold, F. X., & Mariano, R. S. (1995). Comparing Predictive Accuracy. Journal of Business & Economic Statistics.