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Related papers: Local volatility under rough volatility

200 papers

We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an asset arrive according to a Poisson process and have a long…

Mathematical Finance · Quantitative Finance 2026-03-16 Paul P. Hager , Ulrich Horst , Thomas Wagenhofer , Wei Xu

The skew stickiness ratio is a statistic that captures the joint dynamics of an asset price and its volatility. We derive a representation formula for this quantity using the It\^o-Wentzell and Clark-Ocone formulae, and we apply it to…

Mathematical Finance · Quantitative Finance 2026-02-06 Masaaki Fukasawa

We train an LSTM network based on a pooled dataset made of hundreds of liquid stocks aiming to forecast the next daily realized volatility for all stocks. Showing the consistent outperformance of this universal LSTM relative to other…

Statistical Finance · Quantitative Finance 2022-06-29 Mathieu Rosenbaum , Jianfei Zhang

Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…

Computational Finance · Quantitative Finance 2026-03-19 Jimin Lin

The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…

Risk Management · Quantitative Finance 2016-08-16 Ronnie Sircar , Stephan Sturm

Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using…

Quantum Physics · Physics 2025-07-30 Eric Ghysels , Jack Morgan , Hamed Mohammadbagherpoor

The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short…

Pricing of Securities · Quantitative Finance 2017-01-17 Antoine Jacquier , Claude Martini , Aitor Muguruza

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and…

Mathematical Finance · Quantitative Finance 2016-09-08 Omar El Euch , Mathieu Rosenbaum

One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…

Mathematical Finance · Quantitative Finance 2025-12-05 Ofelia Bonesini , Antoine Jacquier , Aitor Muguruza

This paper studies the joint role of long-memory dynamics,rough-volatility behavior, and persistence-based forecasting features in equity volatility modeling. We combine semiparametric long-memory estimation, rough-volatility diagnostics,…

Statistical Finance · Quantitative Finance 2026-05-26 Akash Deep , Nicholas Appiah , Svetlozar T. Rachev

We develop a product functional quantization of rough volatility. Since the quantizers can be computed offline, this new technique, built on the insightful works by Luschgy and Pages, becomes a strong competitor in the new arena of…

Pricing of Securities · Quantitative Finance 2024-03-11 Ofelia Bonesini , Giorgia Callegaro , Antoine Jacquier

This paper proposes a semiparametric stochastic volatility (SV) model that relaxes the restrictive Gaussian assumption in both the return and volatility error terms, allowing them to follow flexible, nonparametric distributions with…

Computation · Statistics 2025-06-03 Yudong Feng , Ashis Gangopadhyay

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential L\'evy models including a Brownian component. As…

Pricing of Securities · Quantitative Finance 2016-05-31 Stefan Gerhold , I. Cetin Gülüm , Arpad Pinter

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the…

Pricing of Securities · Quantitative Finance 2015-05-14 Martin Forde , Antoine Jacquier , Aleksandar Mijatovic

In order to deal with the question of the existence of a calibrated local stochastic volatility model in finance, we investigate a class of McKean--Vlasov equations where a minimal continuity assumption is imposed on the coefficients.…

Probability · Mathematics 2024-10-22 Mao Fabrice Djete

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…

Computational Finance · Quantitative Finance 2016-08-14 Erdinç Akyıldırım , Yan Dolinsky , H. Mete Soner

We develop a variant of rough path theory tailor-made for analyzing a class of financial asset price models known as rough volatility models. As an application, we prove a pathwise large deviation principle (LDP) for a certain class of…

Probability · Mathematics 2023-12-27 Masaaki Fukasawa , Ryoji Takano

We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model. For this we use the Bellaiche \cite{Bel81} heat kernel expansion combined with Laplace's method to integrate over…

Pricing of Securities · Quantitative Finance 2017-02-07 John Armstrong , Martin Forde , Matthew Lorig , Hongzhong Zhang

We introduce a novel distribution-based estimator for the Hurst parameter of log-volatility, leveraging the Kolmogorov-Smirnov statistic to assess the scaling behavior of entire distributions rather than individual moments. To address the…

Mathematical Finance · Quantitative Finance 2026-05-04 Sergio Bianchi , Daniele Angelini

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…

Probability · Mathematics 2021-01-01 Archil Gulisashvili