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1
Content available remote

Share Price Evolution as Stationary, Dependent Continuous-Time Random Walk

100%
Gubiec T., Kutner R.
Acta Physica Polonica A
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2010
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vol. 117
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issue 4
669-672
EN
Simple model of share price evolution, which is an extension of Kehr-Kutner-Binder one and Montero-Masoliver models, is presented. The market empirical data inspired the assumptions of the model. The model seems to be the reference one for the study of the short-range correlations in financial data as it considers the observed correlation over two successive jumps of the financial ant.
2
Content available remote

Reinterpretation of Sieczka-Hołyst Financial Market Model

100%
Denys M., Gubiec T., Kutner R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
513-517
EN
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.
3
Content available remote

Trust in Foreseeing Neighbours - A Novel Threshold Model of Financial Market

100%
Lipski J., Kutner R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
584-588
EN
The three-state agent-based 2D model of financial markets in the version proposed by Giulia Iori in 2002 has been herein extended. We have introduced the increase of herding behaviour by modelling the altering trust of an agent in his nearest neighbours. The trust increases if the neighbour has foreseen the price change correctly and the trust decreases in the opposite case. Our version only slightly increases the number of parameters present in the Iori model. This version well reproduces the main stylized facts observed on financial markets. That is, it reproduces log-returns clustering, fat-tail log-returns distribution and power-law decay in time of the volatility autocorrelation function.
4
Content available remote

Aperiodicity in Equilibrium Systems: Between Order and Disorder

100%
van Enter A.
Acta Physica Polonica A
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2014
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vol. 126
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issue 2
621-624
EN
Spatial aperiodicity occurs in various models and materials. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion and occurrence of aperiodic order in equilibrium statistical mechanics. In particular, we consider some spectral characterisations, and shortly review what is known about the occurrence of aperiodic order in lattice models at zero and nonzero temperatures. At the end some more speculative connections to the theory of (spin-)glasses are indicated.
5
Content available remote

Dynamic Structural and Topological Phase Transitions on the Warsaw Stock Exchange: A Phenomenological Approach

88%
Sienkiewicz A., Gubiec T., Kutner R., Struzik Z.
Acta Physica Polonica A
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2013
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vol. 123
|
issue 3
615-620
EN
We study crash dynamics of the Warsaw Stock Exchange by using minimal spanning tree networks. We identify the transition of the complex network during its evolution from a (hierarchical) power law minimal spanning tree network - representing the stable state of Warsaw Stock Exchange before the recent worldwide financial crash, to a superstar-like (or superhub) minimal spanning tree network of the market decorated by a hierarchy of trees - an unstable, intermediate market state. Subsequently, we observe a transition from this complex tree to the topology of the (hierarchical) power law minimal spanning tree network decorated by several star-like trees or hubs - this structure and topology represent the Warsaw Stock Exchange after the worldwide financial crash, and can be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets.
6
Content available remote

Short Comprehensive Report on the Non-Brownian Stochastic Dynamics at Financial and Commodity Markets

88%
Ciepliński T., Dominiczak A., Kutner R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-24-B-27
EN
In this work we empirically verify the generic breaking of the Central Limit Theorem on the financial and commodity markets. We analysed the distributions of log-returns for typical indices and price of gold, for increasing time horizons. We considered Random Coarse Graining Transformation of the Continuous-Time Random Walk model, which can represent the non-Gaussian price dynamics of underlying assets and the corresponding derivatives, e.g., various options or future contracts. We confirmed that empirical data and predictions of the model quite well agree.
7
Content available remote

Transient properties of a bistable kinetic model with quantum corrections

75%
Ai B.-q., Zheng H., Xie H.-z., Liu L.-g.
Open Physics
|
2006
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vol. 4
|
issue 2
270-276
EN
The transient properties of a Brownian particle moving in a bistable system with quantum corrections are investigated. The Quantum Smoluchowski Equation (QSE) is fully valid for high temperatures; for low temperatures it is valid only in a restricted domain of the state space. The quantum effects in a bistable system stand out for low temperatures. Explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The quantum effects are against the particle moving towards the destination from its original position.
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