English
Related papers

Related papers: Rough volatility: evidence from option prices

200 papers

Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under…

Mathematical Finance · Quantitative Finance 2017-03-16 Omar El Euch , Mathieu Rosenbaum

Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate…

Statistical Finance · Quantitative Finance 2026-05-19 Ranieri Dugo , Giacomo Giorgio , Paolo Pigato

Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…

Statistics Theory · Mathematics 2024-05-29 Ananya Lahiri , Rituparna Sen

This paper shows the relationship between the forward start volatility swap price and the forward start zero vanna implied volatility of forward start options in rough volatility models. It is shown that in the short time-to-maturity limit…

Mathematical Finance · Quantitative Finance 2022-07-22 Elisa Alòs , Frido Rolloos , Kenichiro Shiraya

The Nested factor model was introduced by Chicheportiche et al. to represent non-linear correlations between stocks. Stock returns are explained by a standard factor model, but the (log)-volatilities of factors and residuals are themselves…

Statistical Finance · Quantitative Finance 2025-12-16 Othmane Zarhali , Cecilia Aubrun , Emmanuel Bacry , Jean-Philippe Bouchaud , Jean-François Muzy

Inspired by the activity signature introduced by Todorov and Tauchen (2010), which was used to measure the activity of a semimartingale, this paper introduces the roughness signature function. The paper illustrates how it can be used to…

Econometrics · Economics 2024-01-08 Peter Christensen

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

In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains…

Pricing of Securities · Quantitative Finance 2013-05-16 Jacek Jakubowski , Maciej Wisniewolski

Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…

Econometrics · Economics 2023-02-20 Qiang Liu , Zhi Liu

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to…

Probability · Mathematics 2018-04-12 Eduardo Abi Jaber , Omar El Euch

In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the…

Pricing of Securities · Quantitative Finance 2019-12-17 Jan Pospíšil , Tomáš Sobotka , Philipp Ziegler

We introduce a novel rough Bergomi (rBergomi) model featuring a variance-driven exponentially weighted moving average (EWMA) time-dependent Hurst parameter $H_t$, fundamentally distinct from recent machine learning and wavelet-based…

Mathematical Finance · Quantitative Finance 2025-09-09 Jayanth Athipatla

We estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant…

Statistics Theory · Mathematics 2007-12-18 Arnaud Gloter , Marc Hoffmann

A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the…

Pricing of Securities · Quantitative Finance 2017-06-06 Jean-Pierre Fouque , Yuri F. Saporito

We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a…

Econometrics · Economics 2026-01-21 Mikkel Bennedsen , Kim Christensen , Peter Christensen

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

A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…

Statistical Finance · Quantitative Finance 2025-04-23 Markus Bibinger , Jun Yu , Chen Zhang

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

Other Condensed Matter · Physics 2008-12-02 Rui Vilela Mendes , Maria Joao Oliveira

A technique for on-line estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction.…

Methodology · Statistics 2013-01-15 Rainer Dahlhaus , Jan C. Neddermeyer

We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…

Pricing of Securities · Quantitative Finance 2017-03-29 Sigurd Assing , Yufan Zhao