High-frequency trading model for a complex trading hierarchy
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<italic>t</italic> <sub> <italic>i</italic> </sub>, and the number of shares traded <italic>q</italic>(Δ<italic>t</italic> <sub> <italic>i</italic> </sub>) as two independent but power-law autocorrelated processes, where Δ<italic>t</italic> <sub> <italic>i</italic> </sub> is subordinated to <italic>q</italic>(Δ<italic>t</italic> <sub> <italic>i</italic> </sub>), and Δ<italic>t</italic> <sub> <italic>i</italic> </sub> is more strongly correlated than <italic>q</italic>(Δ<italic>t</italic> <sub> <italic>i</italic> </sub>). These two power-law autocorrelated processes are responsible for the emergence of strong power-law correlations in (a) the total number of shares traded <italic>N</italic>(Δ<italic>T</italic>) and (b) the share volume <italic>Q</italic> <sub>Δ<italic>T</italic> </sub> calculated as the sum of the number of shares <italic>q</italic> <sub> <italic>i</italic> </sub> traded in a fixed time interval Δ<italic>T</italic>. We find that even though <italic>q</italic>(Δ<italic>t</italic> <sub> <italic>i</italic> </sub>) is weakly power-law correlated, due to strong power-law correlations in Δ<italic>t</italic> <sub> <italic>i</italic> </sub>, the (integrated) share volume <inline-formula id="ILM0001"> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_664928_o_ilm0001.gif"/> </inline-formula> 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 ⟨<italic>S</italic>⟩<sub>Δ<italic>T</italic> </sub> and the number of trade occurrences <italic>N</italic> <sub>Δ<italic>T</italic> </sub>, and between ⟨<italic>S</italic>⟩<sub>Δ<italic>T</italic> </sub> and <italic>Q</italic> <sub>Δ<italic>T</italic> </sub>. We find that both results agree with empirical findings.
Year of publication: |
2012
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Authors: | Podobnik, Boris ; Wang, Duan ; Stanley, H. Eugene |
Published in: |
Quantitative Finance. - Taylor & Francis Journals, ISSN 1469-7688. - Vol. 12.2012, 4, p. 559-566
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Publisher: |
Taylor & Francis Journals |
Saved in:
Online Resource
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