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High-frequency trading model for a complex trading hierarchy

Author

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  • Boris Podobnik
  • Duan Wang
  • H. Eugene Stanley

Abstract

Financial markets exhibit a complex hierarchy among different processes, e.g. a trading time marks the initiation of a trade, and a trade triggers a price change. High-frequency trading data arrive at random times. By combining stochastic and agent-based approaches, we develop a model for trading time, trading volume, and price changes. We generate intertrade time (time between successive trades) Δ t i , and the number of shares traded q (Δ t i ) as two independent but power-law autocorrelated processes, where Δ t i is subordinated to q (Δ t i ), and Δ t i is more strongly correlated than q (Δ t i ). These two power-law autocorrelated processes are responsible for the emergence of strong power-law correlations in (a) the total number of shares traded N (Δ T ) and (b) the share volume Q Δ T calculated as the sum of the number of shares q i traded in a fixed time interval Δ T . We find that even though q (Δ t i ) is weakly power-law correlated, due to strong power-law correlations in Δ t i , the (integrated) share volume exhibits strong long-range power-law correlations. We propose that intertrade times and bid--ask price changes share the same volatility mechanism, yielding the power-law autocorrelations in absolute values of price change and power-law tails in the distribution of price changes. The model generates the log-linear functional relationship between the average bid--ask spread ⟨ S ⟩ Δ T and the number of trade occurrences N Δ T , and between ⟨ S ⟩ Δ T and Q Δ T . We find that both results agree with empirical findings.

Suggested Citation

  • Boris Podobnik & Duan Wang & H. Eugene Stanley, 2012. "High-frequency trading model for a complex trading hierarchy," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 559-566, October.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:4:p:559-566
    DOI: 10.1080/14697688.2012.664928
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    Citations

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    Cited by:

    1. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    2. Pyrlik, Vladimir, 2013. "Autoregressive conditional duration as a model for financial market crashes prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6041-6051.
    3. Yu, Jianfeng & Xu, Weidong, 2016. "Pricing turbo warrants under mixed-exponential jump diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 490-501.
    4. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.
    5. repec:eee:phsmap:v:490:y:2018:i:c:p:402-418 is not listed on IDEAS
    6. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.

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