ANALYSIS OF CORRELATION, NETWORK & QUANTUM PRINCIPLES IN FINANCE AND DECISION MAKING

Abstract

The purpose of this thesis is to study the correlation and network behavior of several small cap, mid cap and large cap Indian companies indexed in Bombay Stock Exchange separately. Random matrix theory has been employed to compare the statistical properties of the correlation matrix obtained from the empirical market data. The spectral properties of market data were tested against random matrix predictions and find out some agreement between the distributions of eigenvalues, eigenvector components and the inverse participation ratios for eigenvectors. A bulk of eigenvalues falls within the bounds expected for a random matrix constructed from mutually uncorrelated time series. The eigenvalues below and above the bulk have been investigated. It is observed that few largest and smallest eigenvalues deviate significantly from the bulk, the largest is identified with market mode while the smallest with entanglement characteristics of companies. Entanglement physically means non-separability of two different systems or entities. In the context of companies, it will reveal correlated companies, whose dynamics are intertwined. It is observed that the largest eigenvalue is independent of the dimension of the correlation matrix and dependent upon the capitalization of the stocks. The intermediate eigenvalues that fall between the large and the bulk have been associated with specific business sectors with strong intra-group interactions. The intermediate eigenvalues that fall between the large and the bulk are few in number and lie close to the bulk are associated with specific business sectors with strong intra-group interactions. We propose that this is due to the lack of distinct sector identity in the market to influence the overall market trend. The correlation analysis is carried out to investigate the behavior of stocks during the market crash and it is observed that during crisis stocks belonging to similar or related business sector to move together. Further the internal dynamics of stocks and visualization of financial networks have been investigated, first by constructing Minimum Spanning Tree from the unfiltered correlation matrix. The minimum spanning tree method facilitated to find closest stocks to create a tree. Later market mode and random noise have been removed from the data to show the clustering of stocks into economic sectors based on their proximity. Both methods show absence of clustering of co-moving stocks that belong to same business sector. The analysis of the Indian market crash has been investigated using the minimum spanning tree method and it is observed that during crisis period the stocks are becoming closer than before and after the crisis. ii Further we have also investigated some financial and decision problems using principles of quantum theory. The principal goal of the quantum approach to business and artificial intelligence is to develop a unified theory for functional aspects of the brain that, from one side, could formalize cognitive decision making process in terms of quantum language and, from another side, would suggest a scheme of thinking quantum systems that could be engaged for creating computational intelligence. Quantum computation based on the quantum mechanical nature of physics, which is inherently a parallel distributed processor having the exponential memory capacity and easily trainable, but it has severe hardware limitations. On the other hand the power of artificial neural network is due to its massive parallel, distributed processing of information and nonlinear transformation. Hence attempt is made to explain present understanding and applicability of quantum approach to neural information processing. Quantum computing techniques have successfully explained many computationally hard problems which were impossible in classical computing. Quantum Deutsch’s algorithm has been introduced to predict the financial market price. The Grover’s algorithm for database search has been explained in the case of four qubit system. In some experiments of psychology the classical decision theory is unable to explain the paradoxical departure from logical statements of principle of a sure thing. Such type of paradoxical departure of human behavior in decision making can be explained using the probabilistic mathematical framework of quantum mechanics. An attempt is made to introduce a quantum decision model to explain two stage gambling experiment which violates the principle of sure thing and other decision related problems like merger acquisition problem.