In this thesis, we study the stock dependence based on co-jumps. We construct two separated co-jumps networks according to whether the market jumps or not and use the Spectral Clustering On Ratios-of-Eigenvectors (SCORE) algorithm proposed by Jin et al. [2015] for clustering or community detection. We find the two networks have significantly different clustering results. On the one hand, when the market does not jump, our clustering result can almost perfectly recover some Global Industry Classification Standard (GICS) sectors; on the other hand, it merges the GICS sectors into a community. However, when the market jumps, many stocks co-jump with the market. The clustering result shows relationships from upstream to downstream in a supply chain.

Mathematically, we extend the SC...[ Read more ]

In this thesis, we study the stock dependence based on co-jumps. We construct two separated co-jumps networks according to whether the market jumps or not and use the Spectral Clustering On Ratios-of-Eigenvectors (SCORE) algorithm proposed by Jin et al. [2015] for clustering or community detection. We find the two networks have significantly different clustering results. On the one hand, when the market does not jump, our clustering result can almost perfectly recover some Global Industry Classification Standard (GICS) sectors; on the other hand, it merges the GICS sectors into a community. However, when the market jumps, many stocks co-jump with the market. The clustering result shows relationships from upstream to downstream in a supply chain.

Mathematically, we extend the SCORE from the adjacency matrix to the Poisson matrix (SCORE-P) and prove that SCORE-P enjoys strongly consistent property under some mild assumptions. It benefits from the development of random matrix theory, where the sub-exponential case Bernstein inequality is constructive Tropp [2012].