Market reaction to a bid-ask spread change: A power-law relaxation dynamics

Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N.

doi:10.1103/physreve.80.016112

Cited by 44 publications

(42 citation statements)

References 39 publications

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“…A large number of studies have been focusing on modeling the dynamics of a limit order book, with and without specialists, in financial markets. They comprise both theoretical [2,3,4,5,6,7] and empirical studies [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] devoted to the search for the determinants of several key aspects of price formation, trading process and market organization. These are extremely difficult problems, and their studies can contribute greatly to the success of the modeling of financial markets.…”

Section: Introductionmentioning

confidence: 99%

Diffusive behavior and the modeling of characteristic times in limit order executions

Eisler

Kertész

Lillo

et al. 2009

Quantitative Finance

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We present a study of the order book data of the London Stock Exchange for five highly liquid stocks traded during the calendar year 2002. Specifically, we study the first passage time of order book prices needed to observe a prescribed price change ∆, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones. We find that the distribution of the first passage time decays asymptotically in time as a power law with an exponent λFPT ≈ 1.5. The median of the same quantity scales as ∆ 1.6 , which is different from the ∆ 2 behavior expected for Brownian motion. The quantities TTF, and TTC are also asymptotically power law distributed with exponents λTTF = 1.8 − 2.2 and λTTC = 1.9 − 2.4, respectively. For the medians of the time to fill we observe a scaling proportional to ∆ 1.4 . We outline a simple model, which assumes that prices are characterized by the empirically observed distribution of the first passage time and orders are canceled randomly with lifetimes that are asymptotically power law distributed with a power λLT. The model predicts λTTF = λTTC and we estimate from empirical data λLT ≈ 1.6. We verify that the observed results are not crucially dependent on simplifying assumptions.

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Section: Introductionmentioning

confidence: 99%

Diffusive behavior and the modeling of characteristic times in limit order executions

Eisler

Kertész

Lillo

et al. 2009

Quantitative Finance

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“…However, it seems clear that trade time, especially trade-through time, is not the correct clock, since most of the spread dynamics takes place before a next trade occur, as the order book replenishes itself. Ponzi et al (2009) study a similar problem in the relaxation of the spread. Conditioned on a move of the spread, they measure a relaxation and obtain a power-law behavior of the excess spread in trade time with exponent between 0.4 and 0.5).…”

Section: F Pomponio and F Abergelmentioning

confidence: 99%

Multiple-limit trades: empirical facts and application to lead–lag measures

Pomponio¹,

Abergel²

2013

Quantitative Finance

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Order splitting is a standard practice in trading : traders constantly scan the limit order book and choose to limit the size of their market orders to the quantity available at the best limit, thereby controlling the market impact of their orders. In this article, we focus on the other trades, multiple-limits trades that go through the best available price in the order book, or "trade-throughs". We provide various statistics on trade-throughs: frequency, volume, intraday distribution, market impact... and present a new method for the measurement of lead-lag parameters between assets, sectors or markets.

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“…It is well known that the spread process, s (t), is autocorrelated in time [39,40]. In our models, the spread process, s (t), is represented by a stationary Markov(1) process:…”

Section: Markov Dynamicsmentioning

confidence: 99%

Multiscale Model Selection for High-Frequency Financial Data of a Large Tick Stock by Means of the Jensen–Shannon Metric

Curato

Lillo

2014

Entropy

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Modeling financial time series at different time scales is still an open challenge. The choice of a suitable indicator quantifying the distance between the model and the data is therefore of fundamental importance for selecting models. In this paper, we propose a multiscale model selection method based on the Jensen-Shannon distance in order to select the model that is able to better reproduce the distribution of price changes at different time scales. Specifically, we consider the problem of modeling the ultra high frequency dynamics of an asset with a large tick-to-price ratio. We study the price process at different time scales and compute the Jensen-Shannon distance between the original dataset and different models, showing that the coupling between spread and returns is important to model return distribution at different time scales of observation, ranging from the scale of single transactions to the daily time scale.

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Market reaction to a bid-ask spread change: A power-law relaxation dynamics

Cited by 44 publications

References 39 publications

Diffusive behavior and the modeling of characteristic times in limit order executions

Diffusive behavior and the modeling of characteristic times in limit order executions

Multiple-limit trades: empirical facts and application to lead–lag measures

Multiscale Model Selection for High-Frequency Financial Data of a Large Tick Stock by Means of the Jensen–Shannon Metric

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