Counterparty Risk (III)

In this article, I continue my presentation on Counterparty Risk, namely by exposing some important metrics for credit exposure include the following:?

• Expected mark-to-market (MtM) is the expected value of transaction in the future.?
• Expected exposure (EE) is the amount that is expected to be lost if there is a positive MtM and the counterparty defaults. Expected exposure is higher than expected MtM because the EE considers only positive MtM.
• Potential future exposure (PFE) is an estimate of MtM value at a specific point in the future based on a high confidence level, i.e., the worst exposure that could occur at a given time in the future at a given confidence level.?
• Maximum PFE is the highest PFE value over a stated time frame.
• Expected positive exposure (EPE) is the average EE through time.?

A more graphical representation of the Expected MtM, EE and PFE concepts is presented:

If the choice falls on Credit Exposure, then the reader should be aware of how its profile is impacted by different factors:

• Future uncertainty: the larger the concentration of cash flows in the future, the larger the impact of the uncertainty.
• Periodic cash flows: Conversely, if the cash flows are periodical, then the future uncertainty is lower. Nevertheless, additional risk may exist in case of variables rates, for example.?
• Profile combinations: multiple underlying factors as interest rate and foreign exchange currencies impacting a credit exposure.
• Optionality: potential early exercises also impact the credit exposure profiles.

Based on this, we can now understand the below examples of PFE’s of some common securities:?

Bonds, loans, and repos:?approximately equal to the notional value or 100%, with the upside being attributed to the interest rate risk and potential downside to prepayments:

Swaps: have a peaked shape, from the balance between future uncertainties over payments and the roll-off risk of swap payments over time:

Long option positions: monotonically increase as the option can be deep-in-the-money.

FX products: also monotonically increasing mainly driven by the uncertainty of the final payment given the FX rate risk.?

Credit default swaps:?occurs at a credit event where the notional value less the recovery value is paid (55% in the example):

In our previous articles about Counterparty Risk, we referred the concepts of Netting agreements, that allow two parties to net a set of trades. So, the netting calculation should be done for each scenario before the calculation of EE. The impact of netting, correlation between trades and EE is explicated in the example below for both positive and negative correlation scenarios:

Positive correlations scenarios:

Negative correlation scenarios:

We can see from the examples above that netting benefits are generated when there is negative correlations between trades.

Finally, the choice between Credit Exposure vs value at risk (VaR), already discussed in a previous article, to estimate the risk of loss should consider different factors:?

• Application: VaR is typically only used for risk management, whereas Credit Exposure is also used for pricing and therefore making its quantification more difficult.
• Time horizon:?Credit Exposure can be defined over many maturities while VaR is usually used for short time horizons. Therefore, Credit Exposure requires the modelling of more elements as co-dependence, trends, and implied volatilities.?
• Risk mitigation: Collateral will also reduce exposure, depending on some of key parameters already described in previous article (thresholds, minimum transfer amounts), features of the collateral (delays, value variations, granularity, path dependency) and other associated risks.

Source: Jon Gregory, The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital, 3rd Edition (West Sussex, UK: John Wiley & Sons, 2015).