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.
We develop a Quantile Bayesian Vector Autoregression (QBVAR) to forecast real oil prices across different quantiles of the conditional distribution. The model allows predictor effects to vary across quantiles, capturing asymmetries that standard mean-focused approaches miss. Using monthly data from
Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that explicitly accounts for forecast uncertainty in volatility esti
Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theor
The rough Bergomi (rBergomi) model, characterised by its roughness parameter $H$, has been shown to exhibit multiscaling behaviour as $H$ approaches zero. Multiscaling has profound implications for financial modelling: it affects extreme risk estimation, influences optimal portfolio allocation acros
We introduce the Historical and Dynamic Volatility Ratios (HVR/DVR) and show that equity and index volatilities are cointegrated at intraday and daily horizons. This allows us to construct a VECM to forecast portfolio volatility by exploiting volatility cointegration. On S&P 500 data, HVR is general
This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared errors in Black-Scholes implied volatilities, can produce model-i
Financial markets are complex, non-stationary systems where the underlying data distributions can shift over time, a phenomenon known as regime changes, as well as concept drift in the machine learning literature. These shifts, often triggered by major economic events, pose a significant challenge f
Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, un
This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementati
This paper analyzes realized return behavior across a broad set of crypto assets by estimating heterogeneous exposures to idiosyncratic and systematic risk. A key challenge arises from the latent nature of broader economy-wide risk sources: macro-financial proxies are unavailable at high-frequencies
Optimal execution in financial markets refers to the process of strategically transacting a large volume of assets over a period to achieve the best possible outcome by balancing the trade-off between market impact costs and timing or volatility risks. Traditional optimal execution strategies, such
We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself. Numerical experiments on realistic parameter sets, applied f
Realised volatility has become increasingly prominent in volatility forecasting due to its ability to capture intraday price fluctuations. With a growing variety of realised volatility estimators, each with unique advantages and limitations, selecting an optimal estimator may introduce challenges. I
We model time series of VIX (monthly average) and monthly stock index returns. We use log-Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight is that normalizing monthly stock index returns (dividing them by VIX) makes them much closer to independent identical
In [“1”], we calibrated a one-factor Cheyette SLV model with a local volatility that is linear in the benchmark forward rate and an uncorrelated CIR stochastic variance to 3M caplets of various maturities. While caplet smiles for many maturities could be reasonably well calibrated across the range o
We propose a gradient-based deep learning framework to calibrate the Heston option pricing model (Heston, 1993). Our neural network, henceforth deep differential network (DDN), learns both the Heston pricing formula for plain-vanilla options and the partial derivatives with respect to the model para
We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatilit
We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across
We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with the global shape of SPX smiles. In particular, the at-the-mone
The ongoing Russia-Ukraine conflict between two major agricultural powers has posed significant threats and challenges to the global food system and world food security. Focusing on the impact of the conflict on the global agricultural market, we propose a new analytical framework for tail dependenc