Related papers: The Garman-Klass volatility estimator revisited

We continue the study of the maximum of the scale-inhomogeneous discrete Gaussian free field in dimension two. In this paper, we consider the regime of weak correlations and prove the convergence in law of the centred maximum to a randomly…

Let $B=(B_t)_{t\in {\mathbb{R}}}$ be a two-sided standard Brownian motion. An unbiased shift of $B$ is a random time $T$, which is a measurable function of $B$, such that $(B_{T+t}-B_T)_{t\in {\mathbb{R}}}$ is a Brownian motion independent…

We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $\epsilon$-approximation of its maximum using the smallest…

In this paper we introduce a new methodology to determine an optimal coefficient of penalized functional regression. We assume the dependent, independent variables and the regression coefficients are functions of time and error dynamics…

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…

Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…

It is known from Bramson (1983) that the maximum of branching Brownian motion at time $t$ is asymptotically around an explicit function $m_t$, which involves a first ballistic order and a logarithmic correction. In this paper, we give an…

We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is…

We present an in-depth analysis of the sources of variance in state-of-the-art unbiased volumetric transmittance estimators, and propose several new methods for improving their efficiency. These combine to produce a single estimator that is…

Many estimators of the variance of the well-known unbiased and uniform most powerful estimator $\htheta$ of the Mann-Whitney effect, $\theta = P(X < Y) + \nfrac12 P(X=Y)$, are considered in the literature. Some of these estimators are only…

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over…

Let $B=\{ B_{t}\} _{t\ge 0}$ be a one-dimensional standard Brownian motion. As an application of a recent result of ours on exponential functionals of Brownian motion, we show in this paper that, for every fixed $t>0$, the process given by…

We study the problem of fitting parametrized curves to noisy data. Under certain assumptions (known as Cartesian and radial functional models), we derive asymptotic expressions for the bias and the covariance matrix of the parameter…

The problem of integrated volatility estimation for the solution X of a stochastic differential equation with L{\'e}vy-type jumps is considered under discrete high-frequency observations in both short and long time horizon. We provide an…

We consider unbiased estimation of a sparse nonrandom vector corrupted by additive white Gaussian noise. We show that while there are infinitely many unbiased estimators for this problem, none of them has uniformly minimum variance.…

Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet…

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…

In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than…

We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete-time observations. Specifically, we consider $N$ independent…