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The cross-interval price impact model and its empirical analysis on cryptocurrency order book

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Abstract

The demand for high-frequency algorithmic trading in the cryptocurrency markets is driving the research of price impact mechanisms. We propose the cross-interval price impact model (CIPIM) to explore the advanced or delayed price impact of order book events. The results of the empirical analysis show that neural network structures such as long short-term memory (LSTM) as a specific implementation of CIPIM obtain better concurrent interpretation on price impact than order flow imbalance (OFI) in Cont et al. (J Financ Economet 12(1):47–88, 2014). Meanwhile, the classification version of CIPIM that predicts the direction of Bitcoin price changes tends to work to some extent.

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Notes

  1. See more details about random dropout in Hinton et al. [11] and Srivastava et al. [22].

  2. LSTM can be formally formulated as:

    $$ \begin{array}{@{}rcl@{}} \mathbf{z}_{t} &=& \sigma (\mathbf{W}_{z} \cdot [\mathbf{h}_{t-\delta_{t}}^{\top}, \mathbf{x}_{t}^{\top}]^{\top} + \mathbf{b}_{z}), \\ \mathbf{i}_{t} &=& \sigma (\mathbf{W}_{i} \cdot [\mathbf{h}_{t-\delta_{t}}^{\top}, \mathbf{x}_{t}^{\top}]^{\top} + \mathbf{b}_{i}), \\ \mathbf{o}_{t} &=& \sigma (\mathbf{W}_{o} \cdot [\mathbf{h}_{t-\delta_{t}}^{\top}, \mathbf{x}_{t}^{\top}]^{\top} + \mathbf{b}_{o}), \\ \tilde{\mathbf{c}}_{t} &=& \tanh (\mathbf{W}_{c} \cdot [\mathbf{h}_{t-\delta_{t}}^{\top}, \mathbf{x}_{t}^{\top}]^{\top} + \mathbf{b}_{c}), \\ \mathbf{c}_{t} &=& \mathbf{z}_{t} * \mathbf{c}_{t-\delta_{t}} + \mathbf{i}_{t} * \tilde{\mathbf{c}}_{t}, \\ \mathbf{h}_{t} &=& \mathbf{o}_{t} * \tanh(\mathbf{c}_{t}). \end{array} $$

    See Hochreiter and Schmidhuber [12] for more details. Combining the equation (3), \(\{\mathbf {x}_{t}\}_{t\in [t_{k-1},t_{k}]}\) forms the input variable HX. t and t − δt denote the adjacent moments in [tk− 1,tk]. The output of formula (3) \(\mathbf {h}_{\text {LSTM}}=\mathbf {h}_{t_{k}}\). The parameters of LSTM can be rewritten as Θ = {Wz,bz,Wi,bi,Wo,bo,Wc,bc}.

  3. The subscript t can be considered as the index of the quotes data. In this case, δt = 1, and nk = tk − tk− 1 + 1 counts the number of quote events in [tk− 1,tk]. We will use this notation in the following.

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Acknowledgements

The authors thank the editor and the three anonymous reviewers for reviewing this article for providing valuable suggestions.

Funding

This work is supported by the National Key R&D Program of China (Grant No. 2018YFA0703900), and the National Natural Science Foundation of China (Grant Nos. 11871309, 11371226).

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Authors and Affiliations

  1. Institute for Financial Studies and School of Mathematics, Shandong University, Jinan, 250100, China

    Bin Teng, Sicong Wang, Qinghua Ren, Qi Hao & Yufeng Shi

  2. Shandong Big Data Research Association, Jinan, 250100, China

    Bin Teng, Sicong Wang, Qinghua Ren, Qi Hao & Yufeng Shi

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  1. Bin Teng
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Correspondence to Yufeng Shi.

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Teng, B., Wang, S., Ren, Q. et al. The cross-interval price impact model and its empirical analysis on cryptocurrency order book. Pers Ubiquit Comput 27, 1585–1593 (2023). https://doi.org/10.1007/s00779-021-01651-z

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