Stress Test and Consistent Aggregation of Market, Credit and Transfer Risk by Geometric Arbitrage Theory

Abstract

As an application of Geometric Arbitrage Theory, we apply the derived generator of consistent economic scenarios developed in (Farinelli 2008) to a set consisting of macroeconomic leading indicators, financial market , default probabilities and loss given default time series. The resulting scenarios display consistently possible future evolutions of market and credit risk drivers with equal probability. In particular, PDs and LGDs behavior reflect the credit cycle. Macro-economical stress tests follow, by selecting the paths for which macro-economical variables satisfy required (linear) inequalities whose bounds are given a priori. The portfolio model has following prominent features: - risk factors are observable macroeconomic variables, - multiperiodicity, - full integration of market and credit risk with the possibilities of splitting the different contributions by different risk drivers, - quadratic approximation of the P\&L by utilizing first and second sensitivities to the risk factors, - stress test of PDs, LGDs and P\&L distributions are embedded.