Related papers: Integrated volatility and round-off error

In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are…

We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…

This paper introduces a methodology for constructing a market index composed of a liquid risky asset and a liquid risk-free asset that achieves a fixed target volatility. Existing volatility-targeting strategies typically scale portfolio…

Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters remains a challenge. Here our goal is posterior inference on…

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to…

We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…

We develop further the spot volatility estimator introduced in Hoffmann, Munk and Schmidt-Hieber (2012) from a practical point of view and make it useful for the analysis of high-frequency financial data. In a first part, we adjust the…

A maximum likelihood type estimation of the drift and volatility coefficient parameters in the CIR type model driven by $\alpha$-stable noises is studied when the dispersion parameter $\varepsilon\to0$ and the discrete observations…

With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed…

The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…

We study a new measure of codependency in the second moment of a continuous-time multivariate asset price process, which we name the realized copula of volatility. The statistic is based on local volatility estimates constructed from…

Maximum likelihood estimation applied to high-frequency data allows us to quantify intermittency in the fluctu- ations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency…

This study examine the theoretical and empirical perspectives of the symmetric Hawkes model of the price tick structure. Combined with the maximum likelihood estimation, the model provides a proper method of volatility estimation…

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…

We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the…

We develop a liquidity-sensitive multivariate volatility framework to improve the estimation of time-varying covariance structures under market frictions. We introduce two novel portfolio-level liquidity measures, liquidity jump and…

We focus on extending existing short-rate models, enabling control of the generated implied volatility while preserving analyticity. We achieve this goal by applying the Randomized Affine Diffusion (RAnD) method to the class of short-rate…

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…

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…

The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…