Pruning a Minimum Spanning Tree

This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered affected by noise, based on the study of random networks with the same probability density distribution of the original data. The second technique is to judge the strengh of a connection by its survival rate, which is the amount of time a connection between two stock market indices endure. The idea is that true connections will survive for longer periods of time, and that random connections will not. That information is then combined with the information obtained from the first technique in order to create a smaller network, where most of the connections are either strong or enduring in time

To lag or not to lag? How to compare indices of stock markets that operate at different times

Financial markets worldwide do not have the same working hours. As a consequence, the study of correlation or causality between financial market indices becomes dependent on wether we should consider in computations of correlation matrices all indices in the same day or lagged indices. The answer this article proposes is that we should consider both. In this work, we use 79 indices of a diversity of stock markets across the world in order to study their correlation structure, and discover that representing in the same network original and lagged indices, we obtain a better understanding of how indices that operate at different hours relate to each other

Correlation of financial markets in times of crisis

Using the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world, we show that high volatility of markets is directly linked with strong correlations between them. This means that markets tend to behave as one during great crashes. In order to do so, we investigate several financial market crises that occurred in the years 1987 (Black Monday), 1989 (Russian crisis), 2001 (Burst of the dot-com bubble and September 11), and 2008 (Subprime Mortgage Crisis), which mark some of the largest downturns of financial markets in the last three decades.Comment: 33 pages, 46 figure