Related papers: The sub-fractional CEV model
In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all relevant Hurst indices, i.e. $H \in…
We investigate the valuation of the bid and ask prices for European option under the mixed fractional Brownian motion environment in the presence of superimposed jumps by an independent Poisson process.
We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths,…
Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the…
In this paper we study the moderate deviations principle (MDP) for slow-fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive conditions…
In this paper, we present several path properties, simulations, inferences, and generalizations of the weighted sub-fractional Brownian motion. A primary focus is on the derivation of the covariance function $R_{f,b}(s,t)$ for the weighted…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
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…
Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the Holder regularity is allowed to vary along the paths. In this paper, two kind of multi-parameter extensions of mBm are studied: one is…
In this paper we present a dynamical system to generate Brownian motion based on the Langevin equation without stochastic term and using fractional derivatives, i.e., a deterministic Brownian motion model is proposed. The stochastic process…
In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external…
Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the extraction of geophysical signals. The noise spectrum of these…
The Constant Elasticity of Variance (CEV) model significantly outperforms the Black-Scholes (BS) model in forecasting both prices and options. Furthermore, the CEV model has a marked advantage in capturing basic empirical regularities such…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a…