Calculated Stress Losses for Loan/Derivatives Portfolios

[trigg989]

Hi there,

Not sure why I can't wrap my head around this, but when we calculate EL for a derivatives portfolio (compared to a loan portfolio) we're replacing EAD with EPE x alpha.

The justification for this is that EAD becomes stochastic and is dependent on a level of market variables.

Can I get some more depth to this reasoning?

 

[David Harper CFA FRM]

HI @trigg989

A key difference between a loan and a derivative position is that the loan principal (being funded) is at risk but the derivative's notional is just referenced; e.g., if a vanilla swap references $10.0 million notional, neither counterparty invested that amount, much less anything. Hence the important difference between a funded loan (principal at risk) and an unfunded derivative (where the notional is just referenced). In the derivative portfolio, we do want the EAD, but unlike the loan (where we know how much is at risk and how much is due), it's hard to estimate the forward EAD (not only because the notional is referenced but also because the contract is bilateral, so the credit exposure can be zero, if the value is negative). Jon Gregory is in the syllabus to expand on this, he goes deep, but firstly I would say we are replacing EAD with EPE*α simply because we can't easily observe EAD because it's not the notional. Then, what is EPE? It's the time-weighted average expected exposure (EE) over the simulated life. As Gregory shows, we run simulation(s) of future position values, and at each point in time, the expected exposure, the EE [i.e., the average of each max(value, 0) which itself is a credit exposure] is basically an estimate of the mean/average credit exposure, so at each future point in time the EE is a pretty good estimate of the future EAD. But we have a series of them, we have a forward curve of EEs (aka, the exposure profile, although it call also be represented by forward PFEs). So EE is not a single number. The EPE is the time-averaged EE (i.e., the average of the curve) such that, given we might be looking for a single point estimate, we could do worse than average the EEs into the EPE. In this way, EPE is a best-effort estimate of the EAD, given we can't use the notional. But the EEs are means, so it's also not conservative! If we invest $100 into a loan, we cannot do worse than lose $100. But a derivatives counterparty can do worse than lose the EE/EPE! So, the alpha corrects for that. Just as EAD is arguably conservative, so is EPE*α. Here is Gregory (from his 3rd Ed xVA, on the alpha correction.). I hope that's a helpful start!

8.3.2 The alpha factor and EEPE. The IMM allows the calculation of an accurate exposure distribution at the counterparty level. However, since the regulatory capital calculation for counterparty risk requires a single EAD value per counterparty, a key aspect of the IMM is being able to represent this distribution in a simple way. The key basis for defining EAD was provided by Wilde (2001) who showed that it could be defined via the EPE under the following conditions:

• infinitely large portfolio (number of counterparties) of small exposures (i.e. infinite diversification);
• no correlation of exposures; and
• no wrong-way or right-way risk.

Whilst this is only relevant as a theoretical result, it implies that EPE is a good starting point. Picoult (2002) therefore suggests using a correction to account for the deviations from the idealistic situation above. This correction has become known as the α multiplier and corrects for the finite size and concentration of the portfolio in question. Banks using the IMM have an option to compute their own estimate of α with a methodology that is approved by their regulator and subject to a floor of 1.2. However, this is relatively uncommon and most banks with IMM approval use a supervisory value, which is typically set to 1.4 or more. Table 8.2 shows some published estimates of α and Table 8.3 shows the value as a function of various portfolio inputs using Spreadsheet 8.1. We can see that the following aspects will all cause a decrease in the value of alpha:

• larger portfolio;
• larger average default probabilities;
• larger correlations; and
• higher confidence levels.

... [and he follows here with some actual alpha values based on surveys of banks]" -- Gregory, Jon. The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital (The Wiley Finance Series) (pp. 151-153). Wiley. Kindle Edition.

 

[trigg989]

Thank you so much David. I greatly appreciate the level of detail you provide in your answers.