Risk Aggregation and Economic Capital

Risk management for banks involves risk measurement and risk control at the individual risk level, including market risk for trading books, credit risk for trading and banking books, operational risks and aggregate risk management. In many banks, aggregate risk is defined using a rollup or risk aggregation model; capital, as well as capital allocation, is based on the aggregate risk model. The aggregate risk is the basis for defi ning a bank's economic capital, and is used in value-based management such as risk-adjusted performance management.In practice, different approaches to risk aggregation can be considered to be either one of two types: top-down or bottom-up aggregation. In the top-down aggregation, risk is measured on the sub-risk level such as market risk, credit risk and operational risk; subsequently, risk is aggregated and allocated using a model of risk aggregation. In the bottom-up aggregation model, the sub-risk levels are aggregated bottom-up using a joint model of risk and correlations between the different sub-risks that drive risk factors. In this method the different risk factors for credit, market, operational risk, etc. are simulated jointly.In this paper we consider the linear and copula method of risk aggregation.The copula approach provide a way of isolating the marginal behavior of individual risks from the description of their dependence structure