Volatility estimation under one-sided errors with applications to limit order books


Markus Bibinger from the University of Marburg, Moritz Jirak, from TU Braunschweig and Markus Reiss from Humboldt University Berlin, published a paper using Lobster data. It is titled Volatility estimation under one-sided errors with applications to limit order books and is forthcoming in Annals of Applied Probability.

Abstract: For a semi-martingale X_t, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation ⟨X,X⟩_t is constructed based on observations in the vicinity of X_t. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n^−1/3 as optimal convergence rate in a high-frequency framework with n observations (in mean). We discuss a potential application for the estimation of the integrated squared volatility of an efficient price process X_t from intra-day order book quotes.

A working paper version is found here.

Estimating Spot Cross-Correlations in Asset Returns

Markus Bibinger from the University of Marburg, Nikolaus Hautsch from the University of Vienna, Peter Malec from the University of Cambridge and Markus Reiss from Humboldt University Berlin published a paper using LOBSTER data. It is titled Estimating the Spot Covariation of Asset Prices — Statistical Theory and Empirical Evidence and is forthcoming in the Journal of Business and Economic Statistics.

Abstract: We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al (2014). We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and  general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on  simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.

A working paper version is found here.

Volatility, Information Feedback and Market Microstructure Noise: A Tale of Two Regimes

Torben G. Andersen  from Northwestern University, Gökhan Cebiroglu and Nikolaus Hautsch, both from the University of Vienna, published a CFS working paper using LOBSTER data, titled Volatility, Information Feedback and Market Microstructure Noise: A Tale of Two Regimes.

Abstract: We extend the classical “martingale-plus-noise” model for high-frequency prices by an error correction mechanism originating from prevailing mispricing. The speed of price reversal is a natural measure for informational efficiency. The strength of the price reversal relative to the signal-to-noise ratio determines the signs of the return serial correlation and the bias in standard realized variance estimates. We derive the model’s properties and locally estimate it based on mid-quote returns of the NASDAQ 100 constituents. There is evidence of mildly persistent local regimes of positive and negative serial correlation, arising from lagged feedback effects and sluggish price adjustments. The model performance is decidedly superior to existing stylized microstructure models. Finally, we document intraday periodicities in the speed of price reversion and noise-to-signal ratios.

Read the working paper version here.