A final consideration in terms of defining credit exposure is whether it should be done with respect to risk-neutral or real-world parameters. In the most simple terms, pricing (CVA) should use the former whilst risk management (PFE) the latter. However, the actual situation is more complicated.
Scenario generation for risk management purposes and arbitrage pricing theory use different “measures”. Arbitrage-based pricing uses the so-called risk-neutral measure, which is justified through hedging considerations. Parameters (and therefore probability distributions) such as drifts and volatilities are market-implied and need not correspond to the real distributions (or even comply with common sense). For a risk management application, one does not need to use the risk-neutral measure and should be focused rather on the real-world measure, estimated using, for example, historical data. Risk-neutral parameters are typically used in pricing applications (CVA), whilst real-world parameters generally form the basis of risk management models (PFE). This is the general distinction but there are necessary exceptions, which we discuss below.
The types of parameters to be considered are:
In addition to the above general definitions, effects like mean-reversion should be considered. ...