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High-frequency trading model for a complex trading hierarchy

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  • Boris Podobnik
  • Duan Wang
  • H. Eugene Stanley
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    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.

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    File URL: http://hdl.handle.net/10.1080/14697688.2012.664928
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 12 (2012)
    Issue (Month): 4 (October)
    Pages: 559-566

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    Handle: RePEc:taf:quantf:v:12:y:2012:i:4:p:559-566

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    Cited by:
    1. 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.
    2. 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.

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