Related papers: Volatility estimation from a view point of entropy
We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…
Volatility is a natural risk measure in finance as it quantifies the variation of stock prices. A frequently considered problem in mathematical finance is to forecast different estimates of volatility. What makes it promising to use deep…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
We introduce unbiased estimators for the Shannon entropy and the class number, in the situation that we are able to take sequences of independent samples of arbitrary length.
Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…
We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed It\^{o} semimartingale on a fixed interval when the mesh of the…
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…
The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article we present two new…
We consider a multidimensional It\^o process $Y=(Y_t)_{t\in[0,T]}$ with some unknown drift coefficient process $b_t$ and volatility coefficient $\sigma(X_t,\theta)$ with covariate process $X=(X_t)_{t\in[0,T]}$, the function…
In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…