Professor Jonathan Crook from the University of Edinburgh will present the Department of Statistical Science with a talk entitled, "Stress testing behavioural and macroeconomic risks for credit portfolios".
Abstract: Large banks are required to stress test their credit portfolios annually under Basel II. 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. Simulation requires that the simulated values of the macroeconomic variables are mutually consistent. 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 value at risk when mutually consistent macroeconomic values have been simulated or when behavioural variables have been simulated but not when both are simulated. In this paper we present a method to simulate both behavioural and macroeconomic variables whilst maintaining the correlation structure between them to derive a more comprehensive simulation methodology to stress test a credit portfolio. Specifically, a hazard model of default in terms of behavioural and macroeconomic variables is parameterised. Second, a mixed effects vector autoregressive model relating to behavioural and macroeconomic variables is parameterised. Third, a vector error correction model for the macroeconomic variables is parameterised. Macroeconomic values for a fixed time horizon are gained by simulating the errors of the VECM model. Future values of the behavioural variables for each account are gained by simulating the random effects in the mixed VAR model and using the simulated values of the macroeconomic variables. Hence multiple paths of the behavioural variables for each account are generated consistent with the simulated values of the macroeconomic variables. These simulated values for the behavioural and macroeconomic variables are inserted into the hazard model to derive a distribution of probabilities of default. The method is illustrated using a portfolio of over 100,000 credit card accounts from a major bank. We find the method gives plausible values of value at risk which banks can then use to compute the amount of capital they require.
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