Incorporating behavioural and macroeconomic correlations for the prediction of bank capital for credit risk

Large banks are required to stress test their credit portfolios annually under Basel III. Stress testing credit portfolios to macroeconomic shocks at account level involves parameterising a model predicting probability of default followed by hypothesising specific shocks or by simulation to derive a value at risk (VaR) or expected shortfall (ES), 12 months into the future. Plausible simulation requires that the simulated values of the macroeconomic variables retain their correlated relationships. But the probability of default is also correlated with time-varying behavioural variables, which in turn are correlated with the macroeconomy. Simulation studies have estimated the VaR when mutually consistent macroeconomic values have been simulated or when behavioural variables have been simulated but not when both are simulated. In this article, we present a method to simulate both behavioural and macroeconomic variables into the future whilst maintaining the correlation structure between them to derive a more comprehensive simulation methodology to stress test a credit portfolio.