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The Effect of Clustering in Power-Law Behavior in Financial Systems

Gomrokizadeh, Iman | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55239 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman
  7. Abstract:
  8. Many different scaling laws are observed in financial data. As an example, the distribution of Log-Return of stock prices obey power law, provided relatively short time intervals are considered. In standard statistical physics, scaling laws are observed in critical phenomena, where the system has long-ranged correlations. Within the same context, to arrive at criticality one has to tune some external parameters, such as the temperature. Yet, there are a group of systems that tend towards criticality through their dynamics. Such systems are called self-organised critical systems.There have been proposed many different mechanisms and models to address why power laws are observed in financial systems. In one of the models, the “herd behaviour" of the individuals is proposed to be the underlying reason. It has been shown that if the buying-selling decision of individuals is made within clusters, the distribution of log-return of the price may have a large kurtosis indicating a heavy-tailed distribution. However, it is needed that the system be at the critical point of random percolation threshold to have large kurtosis. In other words, we have to fine-tune some external parameters.In this thesis, we propose a model for both the financial stock price and the clustering of the individuals so that the dynamics naturally take the system to the critical point of the random percolation problem. Therefore, we obtain a self-organised critical system, where both the network and the dynamical variables on the nodes flow towards criticality
  9. Keywords:
  10. Power Law Model ; Critical Phenomena ; Financial Market ; Self Organized Criticality ; Percolation Threshold ; Log-Return of Stock Prices Distribution ; Power Law Behaviour

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