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Information of Liquidity Deeply in the Order Book | March 12, 2018

Although LOBSTER has the capability to generate the entire limit order book, it is currently restricted to a maximum of 200 quote level. As a result a frequently asked question is “Why can’t I generate the whole book?” Besides the data size consideration, the main rational behind this decision is that the liquidity deeply in the book is not likely to be informative.

First, algorithmic traders are not likely to react to deep liquidity, because:

  1. the market data feed of most of trading platform in the industry do not provide the full book information, and
  2. it is not optimal for algorithmic trading strategy to react to deep liquidity – Taking advantage of its speed, the algorithm gets enough time to react when the liquidity is showing up close to the market, say in 5 to 20 quote levels. A model taking an action when the liquidity is still hundreds of levels behind the market, disregarding the platform’s low-latency advantage, is clearly sub-optimal (originally, I use adjective “stupid” which is impolite but likely more proper).

Second, the lower frequency traders are incapable to rationally react to deep liquidity, since

  1. most of them do not have the data feed, and
  2. a human being can hardly analyse more than ten level quotes in a timely fashion.

Third, the deep liquidity in book is typically from uninformative sources:

  1. low-frequency traders who lack the capability to monitor the market in real time, and
  2. the market markers who are obligated to quote on both sides but are not willing to trade on either or both sides.

The the above screen shot from Ivo Zeba’s LOBSTER visualisation tool shows the liquidity distribution and price dynamics over a period.

  • Liquidity A was closed monitored and could be potentially informative in its first showing-up in the book. Since it was in low levels, LOBSTER outputted it “on time”.
  •  Liquidity B was in the mid-range in the book, LOBSTER outputted it. But it might not be really informative for price prediction at its first showing-up.
  • Like liquidity B, liquidity C was also very persistent and getting picked-off. It had not been outputted at the time of showing-up. However, LOBSTER did output it early enough for its price impact into the consideration for a meaningful model.

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Volatility estimation under one-sided errors with applications to limit order books | July 13, 2017

 

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.

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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.

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