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We show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as exp(-c|y|), where c is a positive…

Pricing of Securities · Quantitative Finance 2010-06-21 Vlad Bally , Stefano De Marco

In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…

Mathematical Finance · Quantitative Finance 2024-07-08 Will Hicks

This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main…

Pricing of Securities · Quantitative Finance 2013-07-25 Ole E. Barndorff-Nielsen , Fred Espen Benth , Almut E. D. Veraart

We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the…

Mathematical Finance · Quantitative Finance 2017-02-08 Archil Gulisashvili , Frederi Viens , Xin Zhang

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization…

Pricing of Securities · Quantitative Finance 2012-08-22 Jin Feng , Jean-Pierre Fouque , Rohini Kumar

We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods…

Applications · Statistics 2016-02-02 Georgi Dinolov , Abel Rodriguez , Hongyun Wang

We consider two kinds of stochastic volatility models. Both kinds of models contain a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We discuss discrete time models where for instance a…

Statistics Theory · Mathematics 2014-07-15 Bert van Es , Peter Spreij , Harry van Zanten

In this paper, to cope with the shortage of sufficient theoretical support resulted from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their…

Probability · Mathematics 2020-10-20 Ning Ning , Jing Wu

We introduce a pathwise integration for Volterra processes driven by L\'evy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes, biology, and in environmental finance. Indeed they…

Probability · Mathematics 2016-08-31 Giulia Di Nunno , Yuliya Mishura , Konstiantyn Ralchenko

We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…

Pricing of Securities · Quantitative Finance 2010-10-07 Wolfgang Putschoegl

Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance. While deep neural network models offer promise in approximating the conditional law of such processes,…

Numerical Analysis · Mathematics 2024-05-31 Reza Arabpour , John Armstrong , Luca Galimberti , Anastasis Kratsios , Giulia Livieri

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

Methodology · Statistics 2023-07-20 Almut E. D. Veraart

The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…

Mathematical Finance · Quantitative Finance 2025-10-13 Nicola F. Zaugg , Lech A. Grzelak

We consider a process $X^\ve$ that solves a stochastic Volterra equation with an unknown parameter $\theta^\star$ in the drift function. The Volterra kernel is singular, and includes as an example, $K\_0(u)=c u^{\alpha-1/2} \id{u>0}$ with…

Statistics Theory · Mathematics 2026-05-21 Arnaud Gloter , Nakahiro Yoshida

We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a…

Pricing of Securities · Quantitative Finance 2018-06-20 Aurélien Alfonsi , David Krief , Peter Tankov

In this paper, we introduce a linear stochastic volatility model driven by $\alpha$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its…

Probability · Mathematics 2025-02-04 Xiaotong Li , Wei Liu , Xuerong Mao , Hongjiong Tian , Yue Wu

We consider stochastic volatility dynamics driven by a general H\"older continuous Volterra-type noise and with unbounded drift. For these so-called SVV-models, we consider the explicit computation of quadratic hedging strategies. While the…

Mathematical Finance · Quantitative Finance 2024-07-16 Giulia Di Nunno , Anton Yurchenko-Tytarenko

This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles.…

Probability · Mathematics 2024-10-11 Shanqi Liu , Yaozhong Hu , Hongjun Gao

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…

Physics and Society · Physics 2008-12-02 V. Gontis , B. Kaulakys

The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coefficients are allowed to depend on the whole trajectory of the…

Probability · Mathematics 2026-04-10 Emmanuel Gnabeyeu , Gilles Pagès