PFE & EE Question~

[no_ming]

Hi, Mr. Harper, for the following question, I don't understand why mean & standard deviation is related to EE. Can you help me to have a look?Thank you~

 

[Matthew Graves]

Have you read the corresponding chapter in the FRM books or the BT readings? I suggest you read those first. It's a very basic question.

 

[Dr. Jayanthi Sankaran]

Hi @no_ming,

Expected exposure (EE) is the amount expected to be lost if the counterparty defaults. In other words, the EE will be greater than the Expected MTM, since it concerns only the positive MTM values.

Potential Future Exposure (PFE), on the other hand is the worst exposure we could have at a certain time in the future. In other words, PFE at a 95% confidence level will define an exposure that would be exceeded with a probability of no more than 5%.

While the definition of PFE is exactly the same as VAR, the notable difference in the context of credit exposure, is that it refers to a number that will be normally associated with a gain (exposure), whereas traditional VAR refers to a loss. VAR is trying to predict a worst-case loss, whereas PFE is actually predicting a worst-case gain.

Exposure E = Max(V,0) = Max(u + sigma*Z, 0)
Expected Exposure EE = average of only positive MTM's in the future
Potential Future Exposure (PFE) = u +sigma*NORMSINV(alpha)

Hope that helps!

 

[David Harper CFA FRM]

@no_ming This is a question I wrote (see https://forum.bionicturtle.com/threads/p2-t6-321-credit-exposure-metrics.7154 ) so it is unfortunate that you have obtained it freely cc: @Nicole Manley

 

[no_ming]

Hi @no_ming,

Expected exposure (EE) is the amount expected to be lost if the counterparty defaults. In other words, the EE will be greater than the Expected MTM, since it concerns only the positive MTM values.

Potential Future Exposure (PFE), on the other hand is the worst exposure we could have at a certain time in the future. In other words, PFE at a 95% confidence level will define an exposure that would be exceeded with a probability of no more than 5%.

While the definition of PFE is exactly the same as VAR, the notable difference in the context of credit exposure, is that it refers to a number that will be normally associated with a gain (exposure), whereas traditional VAR refers to a loss. VAR is trying to predict a worst-case loss, whereas PFE is actually predicting a worst-case gain.

Exposure E = Max(V,0) = Max(u + sigma*Z, 0)
Expected Exposure EE = average of only positive MTM's in the future
Potential Future Exposure (PFE) = u +sigma*NORMSINV(alpha)

Hope that helps!

Hello, Dr. Jayanthi Sankaran, where can i find the formula - Exposure E = Max(V,0) = Max(u + sigma*Z, 0), seems i cannot find in the FRM notes book2

 

[edmondclchou]

Please refer to the following links for your questions:

(1) http://www.fincad.com/resources/resource-library/article/counterparty-credit-exposure-swaps
(2) http://www.investopedia.com/articles/optioninvestor/11/understanding-counterparty-risk.asp

Exposure E = Max(V,0) = Max(u + sigma*Z, 0), this reflects positive value of Expected Exposure and depicted the normal distribution formula of its positive value

 

[Dr. Jayanthi Sankaran]

In addition to the great links that @edmondclchou has given above, you can find the formula's for Exposure, Expected Exposure and Potential Future Exposure on Pages 39-40, Appendix 2A, Chapter 2: Defining Counterparty Credit Risk of Jon Gregory's "Counterparty credit risk" - The new challenge for global financial markets, Wiley 2010.

Hope that helps!

 

[no_ming]

Finally, I get the formula from the book provided by @Dr. Jayanthi Sankaran, thanks all
In another word, not only EE, if Sigma and mean increase, PFE, EPE etc. also increase, is that right?

 

[David Harper CFA FRM]

@no_ming Re: In another word, not only EE, if Sigma and mean increase, PFE, EPE etc. also increase, is that right? Yes, if you increase µ or σ then you are shifting or "expanding" (dispersing) the normal distribution, so the x% PFE will increase, in the same way that higher volatility or lower return will increase (absolute) value at risk because there x% tail (quantile) is further into loss territory. In my opinion, EPE is not strictly relevant here because EPE is average EE over time, whereas the above really refers to a single "slice" of time where the distribution characterizes MtM value at that point in time. So to say that EPE is effected might be strictly true (i.e., ceteris paribus to increase EE is presumably to increase EPE), but it is confusing (or at least could be confusing) because it mixes a given time interval (measured with EE or PFE) and a time-weighted measure (EPE). You'll notice my question doesn't included EPE and that's because it's simple. I think it's more important to grok the conceptual differences between these terms. Thanks!