In this work, we study the problem of learning volatility under market microstructure noise. Specifically, consider noisy discrete time observations from a stochastic differential equation and develop novel computational method to learn diffusion coefficient equation. We take nonparametric Bayesian approach, where priori model function as piecewise constant. Its prior is specified via inverse G...

High frequency based estimation methods for a semiparametric pure-jump subordinated Brownian motion exposed to a small additive microstructure noise are developed building on the two-scales realized variations approach originally developed by Zhang et al. (2005) for the estimation of the integrated variance of a continuous Itô process. The proposed estimators are shown to be robust against the ...

In this paper, we address the problem of physical object authentication based on surface microstructure images. The authentication is based on digital content fingerprints computed from the microstructure images. We analyze the impact of camera distortions which follow additive correlated Gaussian noise. The optimal decision rule is derived and the performance is analyzed in the direct and tran...

During supercontinuum formation in nonlinear fiber the presence of a noise seed on the input laser pulse can lead to significant excess noise on the generated output supercontinuum electric field. We relate pulse-averaged moments of this electric-field noise to the measured RF spectrum of the frequency comb formed by the supercontinuum. We present quantitative numerical results for the intrinsi...

After characterizing the Raman scattering in a fused silica polarization-maintaining microstructure optical fiber, we built a fiber-based two-photon light source of high spectral brightness, broad spectral range, and very low noise background at room temperature. The resulting bright low-noise two-photon light can be used for a number of quantum information applications.

Supercontinua generated by femtosecond pulses launched in microstructure fiber can exhibit significant low-frequency (<1-MHz) amplitude noise on the output pulse train. We show that this low-frequency noise is an amplified version of the amplitude noise that is already present on the input laser pulse train. Through both experimental measurements and numerical simulations, we quantify the noise...

OF THE Spot Volatility Estimation of Itô Semimartingales Using Delta Sequences by Weixuan Gao Master of Arts in Statistics Washington University in St. Louis, 2016 Professor José E. Figueroa-López, Chair Abstract: This thesis studies a unifying class of nonparametric spot volatility estimators proposed by Mancini et. al.(2013). This method is based on delta sequences and is conceived to include...

This paper presents a comprehensive empirical evaluation of option-implied and returnsbased forecasts of volatility, in which new developments related to the impact on measured volatility of market microstructure noise and random jumps are explicitly taken into account. The option-based component of the analysis also accommodates the concept of model-free implied volatility, such that the forec...

Default probability is a fundamental variable determining the credit worthiness of a firm and equity volatility estimation plays a key role in its evaluation. Assuming a structural credit risk modeling approach, we study the impact of choosing different non parametric equity volatility estimators on default probability evaluation, when market microstructure noise is considered. A general stocha...