Related papers: The characteristic function of rough Heston models
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the…
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…
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…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…
In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and $\varepsilon$-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend…
Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $\sigma>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we…
We consider convolution-type stochastic Volterra equations with additive Hilbert-valued fractional Brownian motion, $0<H<1$. We find the weak solution to this stochastic Volterra equation, and study its stochastic integral part, the…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
Strongly consistent and asymptotically normal estimators of the Hurst parameter of solutions of stochastic differential equations are proposed. The estimators are based on discrete observations of the underlying processes.
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…
The fractional Brownian motion with index $\alpha$ is introduced to construct the fractional excursion set model. A new mass function with single parameter $\alpha$ is derived within the formalism, of which the Press-Schechter mass function…
We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. The volatility process…
Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u}d\mu(u), \;\; 0\leq t\leq 1{equation} A different…
We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that…
Understanding the statistical laws governing citation dynamics remains a fundamental challenge in network theory and the science of science. Citation networks typically exhibit in-degree distributions well approximated by log-normal…
In this work we study fractal properties of rough differential equations driven by a fractional Brownian motions with Hurst parameter $H>\frac{1}{4}$. In particular, we show that the Hausdorff dimension of the sample paths of the solution…
In this note, we provide a non trivial example of differential equation driven by a fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, whose solution admits a smooth density with respect to Lebesgue's measure. The result is…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…