Nivedita Deo

Analyzing Crisis in Global Financial Indices

We apply the Random Matrix Theory and complex network techniques to 20 global financial indices and study the correlation and network properties before and during the financial crisis of 2008 respectively. We find that the largest eigenvalue deviate significantly from the upper bound which shows a strong correlation between financial indices. By using a sliding window of 25 days we find that largest eigenvalue represent the collective information about the correlation between global financial indices and its trend indicate the market conditions. It is confirmed that eigenvectors corresponding to second largest eigenvalue gives useful information about the sector formation in the global financial indices. We find that these clusters are formed on the basis of the geographical location. The correlation network is constructed using threshold method for different values of threshold θ in the range 0 to 0.9, at θ=0.2 the network is fully connected. At θ=0.6, the Americas, Europe and Asia/Pacific form different clusters before the crisis but during the crisis Americas and Europe are strongly linked. If we further increase the threshold to 0.9 we find that European countries France, Germany and UK consistently constitute the most tightly linked markets before and during the crisis. We find that the structure of Minimum Spanning Tree before the crisis is more star like whereas during the crisis it changes to be more chain like. Using the multifractal analysis, we find that Hurst exponents of financial indices increases during the period of crisis as compared to the period before the crisis. The empirical results verify the validity of measures, and this has led to a better understanding of complex financial markets.

Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings

In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists Kramers degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value Φ±ΔΦ. The external magnetic flux Φ is introduced to make the wave function periodic when the electron circulates around the defect. It is found that this separation occurs due to the effect of the conical curvature on the spin orbit coupling. Further, we find these results are robust to the addition of the Rashba spin orbit interaction which is important for the application to spintronics and nanoelectronics.

Extreme Eigenvector Analysis of Global Financial Correlation Matrices

The correlation between the 31 global financial indices from American, European and Asia-Pacific region are studied for a period before, during and after the 2008 crash. A spectral study of the moving window correlations gives significant information about the interactions between different financial indices. Eigenvalue spectra for each window is compared with the random matrix results on Wishart matrices. The upper side of the spectra outside the random matrix bound consists of the same number of eigenvalues for all windows where as significant differences can be seen in the lower side of the spectra. Analysis of the eigenvectors indicates that the second largest eigenvector clearly gives the sectors indicating the geographical location of each country i.e. the countries with geographical proximity giving similar contributions to the second largest eigenvector. The eigenvalues on the lower side of spectra outside the random matrix bounds changes before during and after the crisis. A quantitative way of specifying information based on the eigenvectors is constructed defined as the “eigenvector entropy” which gives the localization of eigenvectors. Most of the dynamics is captured by the low eigenvectors. The lowest eigenvector shows how the financial ties changes before, during and after the 2008 crisis.