Stochastic behaviour of risk-weighted bank assets under the Basel II capital accord

The primary objective of this paper is to add to the growing debate about the impact of the Basel II Capital Accord (see Base II, June 2004) on the functioning of internationally active banks. A technical contribution is made to this discussion by constructing a stochastic continuous-time model for the dynamics of the total risk-weighted assets (RWAs) of such a bank. RWAs exhibit random behaviour because they partly depend on the uncertain rates of return of bank investments. Also, such assets are weighted by considering the main risks that banks have to bare, viz., credit, operational and market risk. Here the credit risk capital requirement is viewed from the perspective of the internal ratings-based (IRB) approach, operational risk capital is considered within the framework of the standardized approach and a Value-at-Risk (VaR) model describes the capital charge for market risk. Total RWAs (TRWAs) are used to calculate the capital adequacy ratio that is regarded as the most important component of bank supervision and risk management. In particular, according to Basel II, the capital adequacy of banks is determined by the ratio of eligible regulatory capital to TRWAs.