We present backward jump modification of the Continuous-Time Random Walk model or the version of the model driven by the negative feedback [1]. In the frame of the model we describe the stochastic evolution of a typical share price on a stock exchange within a high-frequency time scale.

In the context of the market trading the backward price jump is a reminiscence of such a bid-ask bounce phenomenon where consecutive jumps have the same or almost the same lengths, but opposite signs. We suggested that this correlation dominated the dynamics of a stock market on the tick-by-tick timescale.

The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart. It should be noted that parameters of the model were obtained from separate data sets, so as the comparison of the theoretical velocity autocorrelation function with corresponding empirical curve has no free parameters.

[1] T. Gubiec, R. Kutner: Backward jump continuous-time random walk: An application to market trading, Phys. Rev. E (2010), in print.

1. PRESENTATION: Backward jump Continuous-Time Random Walk on a stock market. What is the true origin of the autocorrelation on the market?, Microsoft Office Document, 2MB

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