Durability of Links between Assets in Financial Markets: Minimal Spanning Trees and Correlations

We investigate hierarchical structure in stock markets according to Minimum Spanning Tree (MST) methods based on correlations between assets. The research was carried out on established (DJIA, DAX, FTSE100) and emerging markets (WIG 20). We consider durability of correlations between assets expressed by using the life-time of correlations between stocks or Minimum Spanning Trees half-life. In both methods durability of correlations depends on price history (time window width Δt). We extend our research on FOREX where the structure of Minimum Spanning Trees depends on basic currencies and reflects geographical connections. On the other hand, according to multistep survival ratio method, the survival of correlations and Minimum Spanning Trees does not depend on basic currency. We also detect a collective behavior and influences between single elements. The optimal window width used to compute correlation coefficients in financial markets is also discussed.