Derivative trading networks: a spectral model for risk identification

This paper develops a spectral model for derivative trading networks in which the trading system’s covariance matrix coincides exactly with its graph Laplacian. The framework captures interconnectedness among dealers by distinguishing between direct linkages arising from transactions and indirect linkages driven by market correlations. By leveraging fundamental Laplacian properties and enforcing impartial treatment of all dealers, the network’s edge weights emerge as an algebraic expression of the weighted node degrees. This configuration, which is instrumental for network reconstruction from aggregate data, is further confirmed to correspond to the minimum Euclidean norm solution obtained from the Moore–Penrose pseudoinverse. This analytical framework permits closed-form expressions for the eigenvalues and eigenvectors, revealing fundamental modes of systemic risk. The spectral analysis uncovers distinct risk patterns, including net exposure neutrality, bipolar movements, core-periphery localization, and extreme risk concentrations. These properties are illustrated through a numerical example. The model also offers a practical tool for regulators and central counterparties, enabling systemic risk assessments based solely on aggregate portfolio variance data without reliance on confidential transaction-level information. Future extensions are proposed to incorporate credit events and default cascades.