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 show the existence and uniqueness of a continuous solution to a path-dependent volatility model introduced by Guyon and Lekeufack (2023) to model the price of an equity index and its spot volatility. The considered model for the trend and activity features can be written as a Stochastic Volterra
In the realm of financial analytics, leveraging unstructured data, such as earnings conference calls (ECCs), to forecast stock volatility is a critical challenge that has attracted both academics and investors. While previous studies have used multimodal deep learning-based models to obtain a genera
The transformer models have been extensively used with good results in a wide area of machine learning applications including Large Language Models and image generation. Here, we inquire on the applicability of this approach to financial time series. We first describe the dataset construction for tw
We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with the quadratic covariation of the latent random process that
We present an approximation method based on the mixing formula (Hull & White 1987, Romano & Touzi 1997) for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option price. It is implemented using a recursive algorithm that all
Starting from a corpus of economic articles from The Wall Street Journal, we present a novel systematic way to analyse news content that evolves over time. We leverage on state-of-the-art natural language processing techniques (i.e. GPT3.5) to extract the most important entities of each article avai
Previously, in [“GR19”], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case λ= 0, which corresponds to a pure power-law kernel. In this paper we extend this solution to the general case of the Mittag-Leffler kernel with λ\geq 0. We provide nume
With the increasing volume of high-frequency data in the information age, both challenges and opportunities arise in the prediction of stock volatility. On one hand, the outcome of prediction using tradition method combining stock technical and macroeconomic indicators still leaves room for improvem
We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we perform experiments in order to gauge the numerical accurac
The covariance between the return of an asset and its realized volatility can be approximated as the difference between two specific implied volatilities. In this paper it is proved that in the small time-to-maturity limit the approximation error tends to zero. In addition a direct relation between
This paper provides a unique approach with AI algorithms to predict emerging stock markets volatility. Traditionally, stock volatility is derived from historical volatility,Monte Carlo simulation and implied volatility as well. In this paper, the writer designs a consolidated model with back-propaga
This paper investigates the forecasting performance of COMEX copper futures realized volatility across various high-frequency intervals using both econometric volatility models and deep learning recurrent neural network models. The econometric models considered are GARCH and HAR, while the deep lear
We study affine stochastic Volterra equations on the cone of symmetric positive semidefinite matrices. For scalar kernels acting entrywise on the matrix dynamics, we establish weak existence by exploiting stochastic invariance results for Volterra equations on convex domains and derive a conditional
Systematic investment strategies are exposed to a subtle but pervasive vulnerability: the progressive erosion of their effectiveness as market regimes change. Traditional risk measures, designed to capture volatility or drawdowns, overlook this form of structural fragility. This article introduces a
This paper is concerned with Merton’s portfolio optimization problem in a Volterra stochastic environment described by a multivariate fake stationary Volterra–Heston model. Due to the non-Markovianity and non-semimartingality of the underlying processes, the classical stochastic control approach ca
The approval of the Bitcoin Spot ETF in January 2024 marked a transformative event in cryptocurrency markets, signaling increased institutional adoption and integration into traditional finance. This study examines Bitcoin’s changing relationships with traditional assets, including equities, gold, a
This paper investigates asymptotically optimal importance sampling (IS) schemes for pricing European call options under the Heston stochastic volatility model. We focus on two distinct rare-event regimes where standard Monte Carlo methods suffer from significant variance deterioration: the limit as
Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices across all strikes and maturities with high accuracy. However,
Financial markets are inherently non-stationary, with shifting volatility regimes that alter asset co-movements and return distributions. Standard portfolio optimization methods, typically built on stationarity or regime-agnostic assumptions, struggle to adapt to such changes. To address these chall
Synthetic time series are essential tools for data augmentation, stress testing, and algorithmic prototyping in quantitative finance. However, in cryptocurrency markets, characterized by 24/7 trading, extreme volatility, and rapid regime shifts, existing Time Series Generation (TSG) methods and benc