Developing New Mathematical Theories for Systemic Risk Contagion in the Nigerian Financial System

Systemic risk in the Nigerian financial system, encompassing interbank lending networks, payment system exposures, and cross-sectoral linkages among banks, insurance companies, pension funds, and capital market operators, poses a fundamental threat to financial stability that existing microprudential tools are theoretically ill-equipped to address. This dissertation develops new mathematical theories for systemic risk measurement and contagion modelling in the Nigerian financial system, making four original theoretical contributions. First, an original network formation model of the interbank lending market is developed based on incomplete information bilateral bargaining, with a theoretical characterisation of the stable network equilibria and their systemic risk properties. Second, a novel stress propagation model using a nonlinear dynamical system on the financial network is developed, and the conditions for a phase transition from contained to cascading failure are characterised through spectral analysis of the Jacobian at the stress propagation equilibrium. Third, an original systemic risk measure termed the Marginal Network Stress Contribution is axiomatically defined and proved to satisfy desirable properties of consistency, monotonicity, and decomposability not simultaneously satisfied by existing measures. Fourth, a macroprudential policy optimisation problem is formulated as a robust control problem on the network dynamical system, with an original theorem characterising the optimal capital surcharge policy. The theoretical framework is calibrated using confidential interbank exposure data from the Central Bank of Nigeria for 2019 to 2023. Keywords: systemic risk, financial network, contagion modelling, macroprudential policy, robust control.