Designing a Model to Investigate the Process of Forming Cluster Fluctuations According to the Fractal Structure in Financial Markets

Subject Areas : Financial Mathematics

Amin Amini Bashirzadeh ¹ , Shahrokh Bozorgmehrian ² , Bahareh Banitalebi Dehkordi ³

1 - دانشگاه آزاد اسلامی شهرکرد
2 - Department of Computer Science, University of Saskatchewan, Saskatoon, SK, Canada
3 - Department of Accounting, Shahrekord branch, Islamic Azad University, Shahrekord, Iran

Received: 2022-11-26 Accepted : 2023-05-02 Published : 2024-04-27

Keywords: Multi-level Multivariate Clustering, Factor-Based Modeling, Cluster Volatility, Fractal Structure of the Market,

Abstract :

Cluster fluctuations and fractal structures are important features of space-time correlation in complex financial systems. However, the microscopic mechanism of creation and expansion of these two features in financial markets remains challenging. In the current research, by using factor-based model design and considering a new interactive mechanism called multi-level clustering, the formation process of cluster fluctuations was investigated with regard to the fractal structure of financial markets. For this purpose, the daily information of the final price of 150 shares that were accepted in the Tehran Stock Exchange, after the final screening, was entered in 5 sections with 30 shares in each section, in the desired model, and they were aggregated in three stock levels., sector and market were measured. Due to the fact that some investors have a longer investment horizon in the stock market and due to the limitation of the investigated time period, the maximum investment horizon of 1000 days has been determined in the model.In addition, the data studied in the research model are from August 2012 to September 2018. The findings of the research showed that the intensity of the tendency of collec-tive behavior at the sector level is much stronger than at the market level. In addition, based on the findings of the research, it was determined that the distribution of simulation eigenvalues in three levels is significantly similar to the distribution of real data. Also, according to the investor's time horizon, the studied series always has a long-term memory for fluctuations. In addi-tion, it was found that long-term memory is directly related to fractal dimen-sions. The findings of this research, in addition to providing a new insight into the space-time correlations of financial markets, show that multi-level conglomeration is one of the mechanisms for creating the microscopic mi-crostructure of such markets. In other words, multi-level collective behavior is an important factor in the occurrence of cluster and fractal fluctuations in the market, and therefore, it should be considered from this point of view in the interpretation of the concept of risk and the definition of risk manage-ment strategies.

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