Related papers: Nonparametric Volatility Density Estimation
Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by \[ dS_{t}=m(\theta_{t})S_{t}…
Autocovariance of the error term in a time series model plays a key role in the estimation and inference for the model that it belongs to. Typically, some arbitrary parametric structure is assumed upon the error to simplify the estimation,…
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…
We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we…
We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…
We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…
We study the sensitivity of the densities of some Kolmogorov like degenerate diffusion processes with respect to a perturbation of the coefficients of the non-degenerate component. Under suitable (quite sharp) assumptions we quantify how…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price.
This paper introduces novel volatility diffusion models to account for the stylized facts of high-frequency financial data such as volatility clustering, intra-day U-shape, and leverage effect. For example, the daily integrated volatility…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…