Fixing Underexposed Snapshots -- Proper Computation of Credit Exposures Under the Real World and Risk Neutral Measures

Abstract

As per regulations and common risk management practice, the credit risk of a portfolio is managed via its potential future exposures (PFEs), expected exposures (EEs), and related measures, the expected positive exposure (EPE), effective expected exposure (EEE) and the effective expected positive exposure (EEPE). Firms use these exposures to set economic and regulatory capital levels. Thus, their values have a big impact on the capital that firms need to hold to manage their risks. Due to the growth of CVA computations, and the similarity of CVA computations to exposure computations, firms find it expedient to compute these exposures under the risk neutral measure. Here we show that such exposures computed under the risk neutral measure are essentially arbitrary. They depend on the choice of numeraire, and can be manipulated by choosing a different numeraire. Even when restricting attention to commonly used numeraires, exposures can vary substantially. As such, it is critical that these calculations be done under the real world measure, not the risk neutral measure.