engleski

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) Dti, and the number of shares traded q(Dti) as two independent but power-law autocorrelated processes, where Dti is subordinated to q(Dti), and Dti is more strongly correlated than q(Dti). 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(DT) and (b) the share volume QDT calculated as the sum of the number of shares qi traded in a fixed time interval DT. We find that even though q(Dti) is weakly powerlaw correlated, due to strong power-law correlations in Dti, the (integrated) share volume QðDTÞ # PDT i¼1 qðDtiÞ 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 functionalrelationship between the average bid–ask spread hSiDT and the number of trade occurrences NDT, and between hSiDT and QDT. We find that both results agree with empirical findings.

subordinated processes; high-frequency data; fractionally integrated processes

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