Heavy tailed distributions in closing auctions

Derksen, Mike; Kleijn, B. J. K.; Vilder, Robin de

doi:10.2139/ssrn.3751309

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…On the theoretical side, Muni Toke (2015) derives the distribution of the exchanged volume and the auction price using a stochastic order flow model during a standard call auction. In the same vein, Derksen et al (2020) propose a stochastic model for call auctions which produces a concave price impact function of market orders; in addition, Derksen et al (2022) build on the previous model to demonstrate the heavy-tailed nature of price and volume in closing auctions. Besides, Donier and Bouchaud (2016) show that under sufficient regularity conditions (continuous price and time) and using a first-order Taylor expansion of supply and demand curves, price impact in Walrasian auctions is linear in the vicinity of the auction price.…”

Section: Introductionmentioning

confidence: 99%

Price impact in equity auctions: zero, then linear

Salek¹,

Challet²,

Toke³

2023

Preprint

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Using high-quality data, we report several statistical regularities of equity auctions in the Paris stock exchange. First, the average order book density is linear around the auction price at the time of auction clearing and has a large peak at the auction price. The linear part comes from fast traders, while the peak is due to slow traders. The impact of a new market order or cancellation at the auction time can be decomposed into three parts as a function of the size of the additional order: (1) zero impact because of the discrete nature of prices; this holds for surprisingly large orders relative to the auction volume (2) linear impact for additional orders up to a large fraction of the auction volume (3) for even larger orders price impact is non-linear, frequently superlinear.

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Section: Introductionmentioning

confidence: 99%

Price impact in equity auctions: zero, then linear

Salek¹,

Challet²,

Toke³

2023

Preprint

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“…The negative skewness is associated, thus, with a positive tail of the distribution being heavier than the negative tail. There are mixed outcomes of the empirical data reported in the literature, including indications of either positive, negative, or neutral skewness as well as the scaling exponent difference between the left and the right tails (in the case of power-law tails) dependent on the analyzed time intervals, markets, and securities (e.g., References [ 14 , 16 , 17 , 20 , 28 , 31 , 36 , 62 , 71 , 94 , 111 , 112 , 113 , 114 , 115 , 116 , 117 , 118 , 119 ]). However, even though a difference between the positive and negative tails exists in the data, it has a much weaker impact on the distribution shape and the related investment risk than the heavy tails.…”

Section: Introductionmentioning

confidence: 99%

Financial Return Distributions: Past, Present, and COVID-19

Wątorek

Kwapień

Dróżdż

2021

Entropy

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We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

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Heavy tailed distributions in closing auctions

Cited by 2 publications

References 21 publications

Price impact in equity auctions: zero, then linear

Price impact in equity auctions: zero, then linear

Financial Return Distributions: Past, Present, and COVID-19

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