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Related papers: Weak error estimates for rough volatility models

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The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the…

Mathematical Finance · Quantitative Finance 2024-06-25 Peter K. Friz , Jim Gatheral

We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based…

Statistics Theory · Mathematics 2018-12-31 Milan Merkle , Yuri F. Saporito , Rodrigo S. Targino

In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the…

Statistics Theory · Mathematics 2007-06-13 Jean-Marc Bardet , Pierre Bertrand

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

We construct a canonical geometric rough path over $d$-dimensional tempered fractional Brownian motion (tfBm) for any Hurst parameter $H > 1/4$ and tempering parameter $\lambda > 0$. The main challenge stems from the non-homogeneous nature…

Probability · Mathematics 2026-04-28 Atef Lechiheb

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

Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…

Statistical Mechanics · Physics 2013-03-11 R. Toenjes , H. Kori

Let $\Phi:\R\rightarrow\R$ be an arbitrary continuously differentiable deterministic function such that $|\Phi|+|\Phi'|$ is bounded by a polynomial. In this article we consider the class of stochastic volatility models in which…

Probability · Mathematics 2012-08-07 Antoine Ayache , Qidi Peng

We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random…

Computational Finance · Quantitative Finance 2024-12-10 Aurélien Alfonsi , Edoardo Lombardo

In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…

Pricing of Securities · Quantitative Finance 2019-10-21 Arunangshu Biswas , Anindya Goswami , Ludger Overbeck

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…

Quantum Physics · Physics 2024-10-23 Guoming Wang , Angus Kan

A class of Gaussian processes generalizing the usual fractional Brownian motion for Hurst indices in (1/2,1) and multifractal Brownian motion introduced in Ralchenko and Shevchenko (Theory Probab Math Stat 80, 2010) and Boufoussi et al.…

Probability · Mathematics 2013-07-08 Jelena Ryvkina

In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path,…

Probability · Mathematics 2025-04-28 Yuzuru Inahama

In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion. This process has been introduced by the second author…

Probability · Mathematics 2011-11-10 Samy Tindel , Jérémie Unterberger

This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by a geometric fractional Brownian rough path $\boldsymbol{\omega}$ with Hurst index…

Probability · Mathematics 2023-03-09 Qiyong Cao , Hongjun Gao , Bjorn Schmalfuss

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…

Mathematical Finance · Quantitative Finance 2025-04-10 Eduardo Abi Jaber , Shaun , Li

We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an…

Statistics Theory · Mathematics 2021-01-06 Mikkel Bennedsen , Ulrich Hounyo , Asger Lunde , Mikko S. Pakkanen

We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform…

Computational Finance · Quantitative Finance 2025-10-23 Keyuan Wu , Tenghan Zhong , Yuxuan Ouyang

In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally,…

Quantum Physics · Physics 2026-02-04 Xabier Oianguren-Asua , Albert Solé , Carlos F. Destefani , Xavier Oriols

This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral…

Probability · Mathematics 2024-10-21 Yuzuru Inahama , Yong Xu , Xiaoyu Yang