Nearest correlation matrix with low-rank structure: a problem from finance

Details

Supervisors

Absil, Pierre-Antoine ; Antoine Vandendorpe

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enThe Nearest Correlation Matrix (NCM) problem has been extensively studied since the early 2000s. However, the increasingly large portfolios managed by financial institutions make it an ever more challenging problem, with growing matrix dimensions. While some institutions choose to partition their portfolio into subsets to reduce the problem size, my supervisor, Antoine Vandendorpe, tasked me with analyzing the limitations of current methods for a specific portfolio of size 18,895, characterized by the full rank of its associated correlation matrix. Many methods found in the literature are therefore ruled out, while the Semismooth Newton Method proposed by Qi and Sun for solving the dual formulation appears promising. The main computational bottleneck lies in the eigenvalue decomposition performed at each iteration. While first-order approximations in the last iterations make the algorithm diverge, early stopping strategies applied during the first iterations of the QR algorithm prove to reduce the CPU time. In cases of reduced rank, promising directions include Golub’s algorithm. Nevertheless, the lack of flexibility of Python's built-in functions prevents drawing definitive conclusions. Finally, approximate methods are also explored, and we developed the new "subspace restriction" and "scaled-subspace restriction" methods.