Volatility is the most forecastable object in finance, which makes its literature a rare pleasure: models compete on real out-of-sample benchmarks and the baseline (HAR-RV) is famously hard to beat. The branches run from the GARCH family through realized measures to implied-vol information and the deep-learning contenders — with the standing question for every new entrant: does it beat HAR under an honest loss function?
flowchart TD ROOT["Volatility Forecasting Research<br>762 papers"] ROOT --> S0["GARCH family & extensions<br>113 papers"] ROOT --> S1["Realized volatility & HAR<br>68 papers"] ROOT --> S2["Implied & options-based<br>257 papers"] ROOT --> S3["Rough & stochastic volatility<br>135 papers"] ROOT --> S4["ML volatility forecasting<br>42 papers"]
762 papers mapped · ranked by rigor-weighted score · regenerated automatically as the daily pipeline scores new papers.
GARCH family & extensions
The parametric core and its many children.
- Synthetic Financial Data Generation for Enhanced Financial Modelling — Holy Grail, rigor 9.0
- Beyond the Mean: Limit Theory and Tests for Infinite-Mean Autoregressive Conditional Durations — Holy Grail, rigor 8.5
- Neural Term Structure of Additive Process for Option Pricing — Holy Grail, rigor 8.0
- Cluster GARCH — Holy Grail, rigor 8.5
- The Three-Dimensional Decomposition of Volatility Memory — Holy Grail, rigor 8.0
- Unified GARCH-Recurrent Neural Network in Financial Volatility Forecasting — Holy Grail, rigor 8.5
- …and 107 more in the garch family & extensions area
Realized volatility & HAR
High-frequency measures and the stubborn baseline.
- Multifractality in Bitcoin Realised Volatility: Implications for Rough Volatility Modelling — Holy Grail, rigor 9.0
- Geometric Deep Learning for Realized Covariance Matrix Forecasting — Holy Grail, rigor 8.0
- Asymptotic Expansions for High-Frequency Option Data — Holy Grail, rigor 8.0
- Jump detection in financial asset prices that exhibit U-shape volatility — Holy Grail, rigor 8.5
- Efficient Sampling for Realized Variance Estimation in Time-Changed Diffusion Models — Holy Grail, rigor 8.0
- High-Frequency Volatility Estimation with Fast Multiple Change Points Detection — Holy Grail, rigor 8.0
- …and 62 more in the realized volatility & har area
Implied & options-based
What option surfaces know that history doesn’t.
- Proof-Carrying No-Arbitrage Surfaces: Constructive PCA-Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates — Holy Grail, rigor 8.5
- A Risk-Neutral Neural Operator for Arbitrage-Free SPX-VIX Term Structures — Holy Grail, rigor 8.5
- Fast reliable pricing and calibration of the rough Heston model — Holy Grail, rigor 8.5
- Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration — Holy Grail, rigor 8.0
- Arithmetic Models for Commodity Futures, Vanilla, and Calendar Spread Options — Holy Grail, rigor 9.0
- Machine Learning Methods for Pricing Financial Derivatives — Holy Grail, rigor 8.0
- …and 251 more in the implied & options-based area
Rough & stochastic volatility
The continuous-time frontier.
- Dynamic Skewness in Stochastic Volatility Models: A Penalized Prior Approach — Holy Grail, rigor 8.5
- A multi-factor model for improved commodity pricing: Calibration and an application to the oil market — Holy Grail, rigor 8.5
- Stochastic Volatility Modelling with LSTM Networks: A Hybrid Approach for S&P 500 Index Volatility Forecasting — Holy Grail, rigor 8.5
- A unified theory of order flow, market impact, and volatility — Holy Grail, rigor 8.0
- End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning — Holy Grail, rigor 8.0
- From rough to multifractal multidimensional volatility: A multidimensional Log S-fBM model — Holy Grail, rigor 7.5
- …and 129 more in the rough & stochastic volatility area
ML volatility forecasting
Networks and hybrids against the classical baselines.
- Neural Lévy SDE for State–Dependent Risk and Density Forecasting — Holy Grail, rigor 8.5
- Constructing Time-Series Momentum Portfolios with Deep Multi-Task Learning — Holy Grail, rigor 8.5
- Deep Learning vs. Statistical Models for Multi-Horizon Price Forecasting of Second-Hand Electronics: A Systematic Benchmark — Holy Grail, rigor 9.0
- Neural Estimation of Irreversibility in Real and Simulated Limit Order Book Paths — Holy Grail, rigor 8.0
- Partial multivariate transformer as a tool for cryptocurrencies time series prediction — Holy Grail, rigor 8.0
- Adaptive Nesterov Accelerated Distributional Deep Hedging for Efficient Volatility Risk Management — Holy Grail, rigor 7.0
- …and 36 more in the ml volatility forecasting area
Evaluation lens for this field: see the guides index · Full hub: /topics/volatility/