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Reinterpretation of Sieczka-Hołyst Financial Market Model

100%

Denys M., Gubiec T., Kutner R.

Acta Physica Polonica A

2013

vol. 123

issue 3

513-517

In this work we essentially reinterpreted the Sieczka-Hołyst model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbors to buy some stocks if agents have an opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents' opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the Sieczka-Hołyst model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach.

Statistical Collapse of Excessive Market Losses

88%

Denys M., Jagielski M., Gubiec T., Kutner R., Stanley H.

Acta Physica Polonica A

2016

vol. 129

issue 5

913-916

We analytically derive superstatistics (or complex statistics) that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) exhibiting transition thresholds. We measure the interevent times between excessive losses (that is, greater than some threshold) and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential. We find that the scaling shape exponent that drives our superstatistics subordinates themselves and a "superscaling" configuration emerges.

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2 Acta Physica Polonica A

1 2016

1 2013

2 Denys M.

2 Gubiec T.

2 Kutner R.

1 Jagielski M.

1 Stanley H.

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Reinterpretation of Sieczka-Hołyst Financial Market Model

Statistical Collapse of Excessive Market Losses