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View article: Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age
Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age Open
The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at…
View article: Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise
Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise Open
We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general s…
View article: Testing for jumps in processes with integral fractional part and jump-robust inference on the Hurst exponent
Testing for jumps in processes with integral fractional part and jump-robust inference on the Hurst exponent Open
We develop and investigate a test for jumps based on high-frequency observations of a fractional process with an additive jump component. The Hurst exponent of the fractional process is unknown. The asymptotic theory under infill asymptoti…
View article: Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities
Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities Open
We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency asymptot…
View article: Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise
Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise Open
We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general s…
View article: Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities
Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities Open
We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency asymptot…
View article: Gumbel convergence of the maximum of convoluted half-normally distributed random variables
Gumbel convergence of the maximum of convoluted half-normally distributed random variables Open
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution. Moti…
View article: Issue Information
Issue Information Open
No abstract is available for this article.
View article: On central limit theorems for power variations of the solution to the\n stochastic heat equation
On central limit theorems for power variations of the solution to the\n stochastic heat equation Open
We consider the stochastic heat equation whose solution is observed\ndiscretely in space and time. An asymptotic analysis of power variations is\npresented including the proof of a central limit theorem. It generalizes the\ntheory from arX…
View article: Common price and volatility jumps in noisy high-frequency data
Common price and volatility jumps in noisy high-frequency data Open
We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on high-frequency data and is robust to market microstructure frictions. For the test, local es…
View article: Volatility estimation for stochastic PDEs using high-frequency\n observations
Volatility estimation for stochastic PDEs using high-frequency\n observations Open
We study the parameter estimation for parabolic, linear, second-order,\nstochastic partial differential equations (SPDEs) observing a mild solution on\na discrete grid in time and space. A high-frequency regime is considered where\nthe mes…
View article: Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence
Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence Open
We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale log asset price process, which is subject to noise and nonsynchronous observations. The estimator is constructed based on a local av…
View article: Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book
Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book Open
An extensive empirical literature documents a generally negative correlation, named the "leverage effect," between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps…
View article: Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book
Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book Open
An extensive empirical literature documents a generally negative correlation, named the "leverage effect," between asset returns and changes of volatility.It is more challenging to establish such a return-volatility relationship for jumps …
View article: Volatility estimation under one-sided errors with applications to limit order books
Volatility estimation under one-sided errors with applications to limit order books Open
For a semi-martingale $X_t$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X, X \rangle_t$ is constructed based on observations in the vicinity of $X_t$. The problem is embedded in a Poiss…
View article: Nonparametric change-point analysis of volatility
Nonparametric change-point analysis of volatility Open
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an Itô semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal…
View article: Nonparametric change-pointanalysis of volatility
Nonparametric change-pointanalysis of volatility Open
This work develops change-point methods for statistics of high-frequency data. The main interest is the volatility of an Itˆo semi-martingale, which is discretely observed over a fixed time horizon. We construct a minimax-optimal test to d…