Market Graph Clustering via QUBO and Digital Annealing

We present a novel technique for cardinality-constrained index-tracking, a common task in the financial industry. Our approach is based on market graph models. We model our reference indices as market graphs and express the index-tracking problem as a quadratic K-medoids clustering problem. We take advantage of a purpose-built hardware architecture to circumvent the NP-hard nature of the problem and solve our formulation efficiently. The main contributions of this article are bridging three separate areas of the literature, market graph models, K-medoid clustering and quadratic binary optimization modeling, to formulate the index-tracking problem as a binary quadratic K-medoid graph-clustering problem. Our initial results show we accurately replicate the returns of various market indices, using only a small subset of their constituent assets. Moreover, our binary quadratic formulation allows us to take advantage of recent hardware advances to overcome the NP-hard nature of the problem and obtain solutions faster than with traditional architectures and solvers.

Comparative Analysis of Financial Network Topology for the Russian, Chinese and US Stock Markets

This paper studies the properties of the Russian stock market by employing the data-driven science and network approaches. The theory of complex networks allows us to build and examine topological network structures of the market with the further identification of relationships between stocks and the analysis of hidden information and market dynamics. In this paper we will present an analysis of structural and topological properties of the Russian stock market using market graph, hierarchical tree, minimum spanning tree approaches. We compare topological properties of the networks constructed for the US and China stock markets with the properties of corresponding networks constructed for the Russian stock market using a dataset spanning over eight years.

Stability Analysis of Company Co-Mention Network and Market Graph Over Time Using Graph Similarity Measures

The aim of the paper is to provide an analysis of news and financial data using their network representation. The formation of network structures from data sources is carried out using two different approaches: by building the so-called market graph in which nodes represent financial assets (e.g., stocks) and the edges between nodes stand for the correlation between the corresponding assets, by constructing a company co-mention network in which any two companies are connected by an edge if a news item mentioning both companies has been published in a certain period of time. Topological changes of the networks over the period 2005–2010 are investigated using the sliding window of six-month duration. We study the stability of the market graph and the company co-mention network over time and establish which of the two networks was more stable during the period. In addition, we examine the impact of the crisis of 2008 on the stability of the market graph as well as the company co-mention network. The networks that are considered in this paper and that are the objects of our study (the market graph and the company co-mention network) have a non-changing set of nodes (companies), and can change over time by adding/removing links between these nodes. Different graph similarity measures are used to evaluate these changes. If a network is stable over time, a measure of similarity between two graphs constructed for two different time windows should be close to zero. If there was a sharp change between the graphs constructed for two adjacent periods, then this should lead to a sharp increase in the value of the similarity measure between these two graphs. This paper uses the graph similarity measures which were proposed relatively recently. In addition, to estimate how the networks evolve over time we exploit QAP (Quadratic Assignment Procedure). While there is a sufficient amount of works studying the dynamics of graphs (including the use of graph similarity metrics), in this paper the company co-mention network dynamics is examined both individually and in comparison with the dynamics of market graphs for the first time.

Network Approaches to Analyze the Dynamics of Financial Markets

Analyzing financial markets requires gathering large amounts of data and determining appropriate methods so that accurate and appropriate conclusions can be drawn. The purpose of this paper is to investigate network approaches to understand large amounts of financial data and the implications of different approaches. Creating a market graph has been used to analyze financial instruments, and prices fluctuations of stocks over a large time period. A market graph is constructed with nodes and edges; nodes represent the quantity of interest, or specific data points, such as stock prices at an instance of time. Edges represent a relationship between one node and another. Creating 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 analysis and the parameter of interest.