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The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…

It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…

Mathematical Finance · Quantitative Finance 2026-01-06 Nicola F. Zaugg , Leonardo Perotti , Lech A. Grzelak

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a…

Statistics Theory · Mathematics 2012-11-29 Jean-Marc Bardet , Donatas Surgailis

We test methods for measuring and characterizing rough profiles with emphasis on measurements of the self-affine roughness exponent, and describes a simple test to separate between roughness exponents originating from long range…

Statistical Mechanics · Physics 2007-07-13 Jan Øystein Haavig Bakke , Alex Hansen

The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…

Statistical Finance · Quantitative Finance 2015-05-08 Gordon J. Ross

In this paper similar to [P. Carr, A. Itkin, 2019] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both…

Computational Finance · Quantitative Finance 2023-09-27 Andrey Itkin

We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) $B_t$ with Hurst parameter $H>1/2$, where the integrands are vector fields…

Probability · Mathematics 2016-12-16 Yohaï Maayan , Eddy Mayer-Wolf

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2020-08-03 Xi Geng , Cheng Ouyang , Samy Tindel

The linear fractional stable motion (LFSM) extends the fractional Brownian motion (fBm) by considering $\alpha$-stable increments. We propose a method to forecast future increments of the LFSM from past discrete-time observations, using the…

Methodology · Statistics 2026-05-12 Matthieu Garcin , Karl Sawaya , Thomas Valade

Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in…

Probability · Mathematics 2019-02-22 Yi Chen , Jing Dong , Hao Ni

We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra…

Mathematical Finance · Quantitative Finance 2023-11-14 Giacomo Giorgio , Barbara Pacchiarotti , Paolo Pigato

We empirically analyze the scaling properties of daily Foreign Exchange rates, Stock Market indices and Bond futures across different financial markets. We study the scaling behaviour of the time series by using a generalized Hurst exponent…

Statistical Mechanics · Physics 2008-12-02 T. Di Matteo , T. Aste , M. M. Dacorogna

The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…

Statistical Finance · Quantitative Finance 2016-09-08 Sergey S. Stepanov

Stochastic roughness is widespread feature of natural surfaces and is an inherent by-product of most fabrication techniques. In view of rapid development of microfluidics, the important question is how this inevitable evil affects the…

Fluid Dynamics · Physics 2019-01-18 Vladimir Parfenyev , Sergey Belan , Vladimir Lebedev

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…

Probability · Mathematics 2008-12-02 Rui Vilela Mendes , M. J. Oliveira

This paper provides several statistical estimators for the drift and volatility parameters of an Ornstein-Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at discrete time…

Probability · Mathematics 2017-03-29 Yaozhong Hu , David Nualart , Hongjuan Zhou

The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. We present a simple, analytically tractable model which fills the gap…

In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…

Probability · Mathematics 2018-05-15 Oussama Amine , David R. Baños , Frank Proske

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…

In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dY_{s}^{(1)}$% , where $u$ is a $\beta$-H\"older continuous process with $\beta > 1-H$ and…

Probability · Mathematics 2018-02-28 Salwa Bajja , Khalifa Es-Sebaiy , Lauri Viitasaari