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Network Approaches To Analyze The Dynamics Of Financial Markets

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Title:
Network Approaches To Analyze The Dynamics Of Financial Markets
Series Title:
19th Annual Undergraduate Research Symposium
Creator:
Lochner, Miranda
Language:
English
Physical Description:
Undetermined

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Center for Undergraduate Research
Center for Undergraduate Research
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Conference papers and proceedings
Poster

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Abstract:
Analyzing financial markets requires gathering large amounts of data which can be difficult to analyze or draw conclusions from. The purpose of this paper is to investigate possible network approaches used to help break down large amounts of financial data. To analyze data, a market graph must be constructed with nodes and edges. Creating a market graph has been used to analyze financial instruments, and prices fluctuations of stocks over a large period. Nodes represent specific data points like stock prices at an instance of time. Creating the edges can be accomplished through many different approaches including correlation coefficients, power law, and minimum spanning tree. Pearson’s correlation coefficient can be used to relate a set of two data points and can be further filtered through a minimum threshold value. The power law graph is another unique way to relate data points to one another. The power law graph creates edges among nodes by considering a probability and the binomial distribution. The power law graph has powerful implications on network analysis because it concludes that the degree distribution, the number of connections a node has to other nodes, is represented as an exponential relationship. A minimum spanning tree is a hierarchical method used to analyze market graphs. A minimum spanning tree clusters data by partitioning data appropriately. Overall, many methods are defined to establish a market graph depending on the purpose of the data analysis. ( en )
General Note:
Research authors: Miranda Lochner - University of Florida
General Note:
University Scholars Program
General Note:
Faculty Mentor: Analyzing financial markets requires gathering large amounts of data which can be difficult to analyze or draw conclusions from. The purpose of this paper is to investigate possible network approaches used to help break down large amounts of financial data. To analyze data, a market graph must be constructed with nodes and edges. Creating a market graph has been used to analyze financial instruments, and prices fluctuations of stocks over a large period. Nodes represent specific data points like stock prices at an instance of time. Creating the edges can be accomplished through many different approaches including correlation coefficients, power law, and minimum spanning tree. Pearson’s correlation coefficient can be used to relate a set of two data points and can be further filtered through a minimum threshold value. The power law graph is another unique way to relate data points to one another. The power law graph creates edges among nodes by considering a probability and the binomial distribution. The power law graph has powerful implications on network analysis because it concludes that the degree distribution, the number of connections a node has to other nodes, is represented as an exponential relationship. A minimum spanning tree is a hierarchical method used to analyze market graphs. A minimum spanning tree clusters data by partitioning data appropriately. Overall, many methods are defined to establish a market graph depending on the purpose of the data analysis. - Center for Undergraduate Research, University Scholars Program

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University of Florida
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Copyright Miranda Lochner. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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Network Approaches to Analyze the Dynamics of Financial Markets Introduction The purpose of this research is to compile a review of methods used to break down large amounts of financial data through network approaches Financial data can be immense, and therefore hard to analyze ; a solution is a network approach through the construction of a market graph Miranda Lochner 1 Panagote Pardalos 2 1,2 Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL Concept of Market Graph Market graphs are comprised of a set of nodes and a set of vertices Nodes represent the quantity of interest, such as a current stock pricing, transactions, credit relations, etc 1 The goal of a network graph is to link the nodes with weighted edges Each edge illustrates a relationship between one node and another 1 Creation of edges by Correlation Coefficient : 1 Where and represent the entity being analyzed The { } brackets represent the expected value An example, where N is the total number of nodes in the graph [ 1 ] Battiston S Glattfelder J Garlaschelli D and Caldarelli G (n d ) The Structure of Financial Networks [ 2 ] C X Nie dimension of financial Physica A : Statistical Mechanics and its Applications [ 3 ] A V Aho J E Hopcroft, and J D Ullman Data Sructures and Algorithms [ 4 ] K Sorensen and P Pardalos "Clustering in Financial Markets [ 5 ] V Boginski S Butenko and P M Pardalos Statistical analysis of financial networks [ 6 ] R Xu, W K Wong, G Chen, and S Huang, Characteristics of the Hong Kong Stock Market : A Test based P threshold Approach to Understanding Network Complexity References Power Law Graph Association Degree Distribution: The amount of edge connections a single node has. Erds and Renyi proposed creating edges by using an independent probability p. 4 By denoting a graph G, with p edges, and n nodes as G( n,p ), Erds and Renyi concluded the degree distribution for any particular node to follow a Binomial distribution which would resemble: 4 As n np becomes a constant, and the Binomial distribution becomes a Poisson distribution: 1. Assign distances between the vertices so that the shortest is the distance and the largest is the correlation between two vertices. 2. Rank these distances from the shortest to the longest. the vertices. 4. Iterate until you find an edge that would form a loop. In this case, jump to the next distance (if necessary repeat). 5. Stop when all the vertices have been considered. Minimum Spanning Tree Procedure 1 Minimum Spanning Tree Hierarchical analysis method Distance matrix, each entry, is equal to: 2 Figure 2: Display of Power Law 5 Figure 3: Example of Market Graph 6 Acknowledgements I would like to thank Dr. Pardalos for being the faculty mentor for this project. Figure 1: Example of Possible Error 3 Conclusion The three most common network approaches used to analyze large sets of financial data are the minimum spanning tree, the power law graph, and Correlation Coefficient The minimum spanning tree draws a network by using distances and correlations between nodes to cluster data into different partitions The power law graph is an important method because it implicates an exponential relationship for a degree distribution Correlation Coefficient is another common method used because the market graph can be filtered by different threshold values, thus affecting the structure of the graph