Fixing Risk Neutral Risk Measures

Abstract

In line with 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). Notably, firms use these exposures to set economic and regulatory capital levels. Their values have a big impact on the capital that firms need to hold to manage their risks.

Due to the growth of credit valuation adjustment (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 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. The numeraire can even be chosen in such a way as to pass backtests. Even when restricting attention to commonly used numeraires, exposures can vary by a factor of two or more. As such, it is critical that these calculations be carried out under the real world measure, not the risk neutral measure. To help rectify the situation, we show how to exploit measure changes to efficiently compute real world exposures in a risk neutral framework, even when there is no change of measure from the risk neutral measure to the real world measure. We also develop a canonical risk neutral measure that can be used as an alternative approach to risk calculations.

Keywords: Credit risk, Regulation, Credit exposure, Basel, Dodd-Frank, PFE, EE, EPE, EEPE, Risk neutral measure, Real world measure, CVA, Credit valuation adjustment, Option modeling, Equivalent martingale measure, Change of measure, Expected exposure, Potential future exposure

JEL Classification: G18, G13, G28, G24, E58, G21