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Related papers: Functional quantization of rough volatility and ap…

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Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the…

Pricing of Securities · Quantitative Finance 2018-10-09 Christian Bayer , Benjamin Stemper

We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in…

Mathematical Finance · Quantitative Finance 2021-06-15 Martino Grasselli , Andrea Mazzoran , Andrea Pallavicini

The quadratic rough Heston model provides a natural way to encode Zumbach effect in the rough volatility paradigm. We apply multi-factor approximation and use deep learning methods to build an efficient calibration procedure for this model.…

Computational Finance · Quantitative Finance 2022-05-31 Mathieu Rosenbaum , Jianfei Zhang

We study the small-time behaviour of the rough Bergomi model, introduced by Bayer, Friz and Gatheral (2016), and prove a large deviations principle for a rescaled version of the normalised log stock price process, which then allows us to…

Probability · Mathematics 2019-07-10 Antoine Jacquier , Mikko S. Pakkanen , Henry Stone

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

In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…

Mathematical Finance · Quantitative Finance 2020-08-05 Christian Bayer , Jinniao Qiu , Yao Yao

We consider the pricing of VIX options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate…

Computational Finance · Quantitative Finance 2025-01-28 Florian Bourgey , Stefano De Marco

We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and…

Mathematical Finance · Quantitative Finance 2020-11-03 Chloe Lacombe , Aitor Muguruza , Henry Stone

The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the…

Mathematical Finance · Quantitative Finance 2022-08-01 Fabien Le Floc'h

Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a…

Pricing of Securities · Quantitative Finance 2019-12-04 Giorgia Callegaro , Lucio Fiorin , Andrea Pallavicini

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…

Mathematical Finance · Quantitative Finance 2017-12-08 Anatoliy Swishchuk , Zijia Wang

In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all…

Pricing of Securities · Quantitative Finance 2022-12-16 Peter K. Friz , Thomas Wagenhofer

In this paper we use convolutional neural networks to find the H\"older exponent of simulated sample paths of the rBergomi model, a recently proposed stock price model used in mathematical finance. We contextualise this as a calibration…

Computational Finance · Quantitative Finance 2019-07-30 Henry Stone

This paper advances interest rate modeling in the post-LIBOR era by introducing rough stochastic volatility into the Forward Market Model (FMM). We establish a rigorous asymptotic expansion of swaption implied volatility, connecting the FMM…

Mathematical Finance · Quantitative Finance 2025-10-01 Reo Adachi , Masaaki Fukasawa , Naoki Iida , Mitsumasa Ikeda , Yo Nakatsu , Ryota Tsurumi , Tomohisa Yamakami

We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for…

Computational Finance · Quantitative Finance 2025-07-17 Peter K. Friz , William Salkeld , Thomas Wagenhofer

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…

Pricing of Securities · Quantitative Finance 2019-08-02 Raul Merino , Jan Pospíšil , Tomáš Sobotka , Tommi Sottinen , Josep Vives

In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…

Computational Finance · Quantitative Finance 2023-02-27 Camilla Damian , Rüdiger Frey

Existing deep learning-based calibration scheme for rough volatility models predominantly rely on supervised learning frameworks, which incur significant computational costs due to the necessity of generating massive synthetic training…

Computational Finance · Quantitative Finance 2026-01-22 Changqing Teng , Guanglian Li

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…

Statistical Finance · Quantitative Finance 2021-01-06 Mikkel Bennedsen , Asger Lunde , Mikko S. Pakkanen

Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal…

Statistics Theory · Mathematics 2019-05-20 Masaaki Fukasawa , Tetsuya Takabatake , Rebecca Westphal