Volatility is the most forecastable quantity in finance — unlike returns, it clusters, mean-reverts, and leaves a measurable footprint in high-frequency data. This hub collects the modeling lineage from GARCH through realized volatility built on intraday data, to rough volatility and the modern deep-learning forecasters, along with VIX and variance-risk-premium research.
Because volatility forecasting has real benchmarks, rigor is easier to judge here than elsewhere: a serious paper compares against HAR-RV (the stubborn workhorse baseline) on out-of-sample data, not just against its own ablations. Watch also for the evaluation-loss trap — rankings of volatility models flip depending on whether you score them with MSE, QLIKE, or economic value in an options or risk-targeting strategy, and good papers say so explicitly.
Related hubs: Options & Derivatives, Risk Management, Machine Learning for Forecasting.
This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning. The approach augments the neural-network input representation with geometric features derived from the stochastic diff
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a
We examine whether model-based spot volatility estimators extracted from traded options data enhance the predictive power of the Heterogeneous Autoregressive (HAR) model for realized volatility. Specifically, we infer spot volatility under the rough stochastic volatility model via an iterative two-s
Limit order books can transition rapidly from stable to stressed conditions, yet standard early-warning signals such as order flow imbalance and short-term volatility are inherently reactive. We formalise this limitation via a three-regime causal data-generating process (stable $\to$ latent build-up
In this work, we investigate the market-making problem on a trading session in which a continuous phase on a limit order book is followed by a closing auction. Whereas standard optimal market-making models typically rely on terminal inventory penalties to manage end-of-day risk, ignoring the signifi
This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is key to risk-manage not only vanilla FX option books, but also more exotic derivatives which are typically valued with l
Financial markets exhibit an apparent paradox: while directional price movements remain largely unpredictable–consistent with weak-form efficiency–the magnitude of price changes displays systematic structure. Here we demonstrate that real-time order-flow entropy, computed from a 15-state Markov tran
The finite sample effect on the Hurst exponent (HE) of realized volatility time series is examined using Bitcoin data. This study finds that the HE decreases as the sampling period $Δ$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $Δ\rightarrow 0
We study the dynamic investment decisions of investors who prioritise specific quantiles of outcomes over their expected values. Downside-focused agents targeting low quantiles reduce risk in states with high variance, while those with a preference for high quantiles concentrate in sleeves with high
This study investigates the application of machine learning techniques, specifically Neural Networks, Random Forests, and CatBoost for option pricing, in comparison to traditional models such as Black-Scholes and Heston Model. Using both synthetically generated data and real market option data, each
The stock market is extremely difficult to predict in the short term due to high market volatility, changes caused by news, and the non-linear nature of the financial time series. This research proposes a novel framework for improving minute-level prediction accuracy using semantic sentiment scores
This paper develops a Bayesian Generalised Pareto Regression (GPR) model to forecast extreme losses in Indian equity markets, with a focus on the Nifty 50 index. Extreme negative returns, though rare, can cause significant financial disruption, and accurate modelling of such events is essential for
This study evaluates the scale-dependent informational efficiency of stock markets using the Financial Chaos Index, a tensor-eigenvalue-based measure of realized volatility. Incorporating Granger causality and network-theoretic analysis across a range of economic, policy, and news-based uncertainty
Volatility forecasting is essential for risk management and decision-making in financial markets. Traditional models like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) effectively capture volatility clustering but often fail to model complex, non-linear interdependencies between
The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hed
There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic volatility (variance of price). The goal of the research is to gener
A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically estimated, via a joint loss function, whilst extending existi
In this study, we examine the fluctuation in the value of the Great Britain Pound (GBP). We focus particularly on its relationship with the United States Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15, 2018, to June 15, 2023, we apply various mathematical models to asses
Option contracts on two underlying assets within uncertain volatility models have their worst-case and best-case prices determined by a two-dimensional (2D) Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with cross-derivative terms. This paper introduces a novel ``decompose and in
This paper introduces SpotV2Net, a multivariate intraday spot volatility forecasting model based on a Graph Attention Network architecture. SpotV2Net represents assets as nodes within a graph and includes non-parametric high-frequency Fourier estimates of the spot volatility and co-volatility as nod