A Theoretical Framework for Integrated Risk Management in Nigerian Commercial Banks Under Basel III Requirements

The implementation of Basel III capital adequacy standards in Nigeria, mandated by the Central Bank of Nigeria's revised banking supervision framework, requires commercial banks to develop mathematically rigorous integrated risk measurement systems that capture the interdependence of credit, market, and operational risks. This dissertation develops an original theoretical framework for integrated risk measurement and management that addresses the fundamental limitation of current practice: the summation of independently measured risk capital charges ignores the diversification and amplification effects of risk interdependence. The framework introduces a novel multi-risk copula model that jointly characterises the dependence structure of credit loss, trading book mark-to-market loss, and operational loss distributions using a vine copula architecture parameterised from historical loss data of five systematically important Nigerian banks over 2010 to 2023. A theoretical contribution is the proof that under this dependence structure, the aggregate Value-at-Risk is bounded above by a function of the individual risk VaRs and the upper tail dependence coefficient, providing a tractable analytical bound for regulatory capital estimation. The framework further develops a dynamic risk allocation mechanism using Euler capital allocation that is proved to satisfy both full allocation and symmetry axioms. Application to a representative large Nigerian bank demonstrates that integrated capital under the proposed framework is 23 percent lower than the simple sum of standalone capital charges, without reduction in actual risk coverage. Keywords: integrated risk management, copula model, Basel III, Value-at-Risk, Nigerian banking.