Expected Exposure & Counter Party PD

[Biju]

Hi David/All,
This may be a trivial question..but a bit not clear to me .When going through the Wrong Way risk where Conditional EE is discussed..

Question 1)
Expected Exposure in General terms=Avg ( +ve MTM ) counter party owes to the bank
If we take an IR Swap example the above Unconditional EE should be same when we have IRS contract with two counterparties of varying credit quality given the initial terms (Fixed/Floating) same?
The Counterparty Risk ( ~ EE * PD*LGD) will be high with lower grade counterparty .
Please confirm

Question 2)
When we say Conditional EE .In the above IRS example the EE going to be same (depending on systematic factors like Interest Rates/FX ..) ? How does the EE vary between counter parties?Are we referring the initial terms of contract (Fixed/Floating) will be different based on the Credit grade of counter party and hence the conditional EE changes

Thanks
Biju

 

[David Harper CFA FRM]

Hi @Biju

Apologies but I don't understand your questions because I don't exactly understand what you mean by "should be the same" (in Q1) and "going to be the same" (in Q2). Which is okay, I've learned that sometimes the hard part is just formulating the question ...or it could always be that I am just missing something in my reading. (I also can't tell if you are referring to statements in our notes, questions or Gregory's source). I would start by taking a step back to basic terms here. Below is Gregory's chart from his spreadsheet 15.1 (wrong way risk) which is similar to his Fig 15.1 (XLS here at http://trtl.bz/gregory-15-xls). Symbolically (without summation details), as you write, regular unconditional CVA ~= EE*PD*LGD such that, as the counterparty's credit rating grade (credit quality) deteriorates the (unconditional) PD increases and CVA increases to reflect an increase in the counterparty risk. (question 1 may be partiallly true but i don't understand the use of "same")

With respect to an IRS, our key job is to understand what wrong-way risk means. In general, WWR is a correlation between exposure and PD; it's bad for us if the default probability increases when the exposure increases. When there is no wrong way risk, EE and PD are independent; if wrong-way risk is present, then EE is positively correlated with PD. Just as correlated EAD and PD increase EL, this positive correlation increases the CVA as a (complicated) product of correlated EE and PD. But there are several ways to try to model this. Gregory's self-described SIMPLE approach is to replace the EE with a conditional EE; i.e., a greater EE conditional on default, as illustrated below. Maybe to your question #2, this is all still within the unilateral CVA: it concerns the institution's exposure to the counterparty's risk. As Dowd mentions, it should be included in both sides so that symbollically in the BCVA = EE*PD(c)*LGD(c) - NEE*PD(i)*LGD(i) both EE and NEE are replaced with conditional exposures. I hope that's helpful start ....

 

[Biju]

Hi David,

Apologies for not having clarity on the question and thanks for detailed response.
My question may be a basic understanding/definition of EE

In the context of Wrong Way Risk (WWR) I understand that Various factors would have lead to an increase EE (moving in favour of bank and adverse to counterparty) and these factors may also have increased the PD of Counterparty..Hence the WWR

My question was around basic definition of EE and trying to seperate it from definition of CounterParty Risk
The Various factors that may led to an increase in EE ..If we take an example,in the case of an IRS I thought these are systematic factors (like FX Rate,IR rates) and not the Credit quality/PD of the counterparty.Because EE=avg(+ve MTM).EE will increase at the same rate with two counterparties having different Grade.I thought the Credit Grade/PD of the counterparty will increase Counterparty Risk and not EE ?Please correct me If am wrong here.

Basically I am trying to differentiate the definition of EE & Counterparty risk

Hope the question is more clear now

Thanks
Biju

 

[bpdulog]

Hi David,

Apologies for not having clarity on the question and thanks for detailed response.
My question may be a basic understanding/definition of EE

In the context of Wrong Way Risk (WWR) I understand that Various factors would have lead to an increase EE (moving in favour of bank and adverse to counterparty) and these factors may also have increased the PD of Counterparty..Hence the WWR

My question was around basic definition of EE and trying to seperate it from definition of CounterParty Risk
The Various factors that may led to an increase in EE ..If we take an example,in the case of an IRS I thought these are systematic factors (like FX Rate,IR rates) and not the Credit quality/PD of the counterparty.Because EE=avg(+ve MTM).EE will increase at the same rate with two counterparties having different Grade.I thought the Credit Grade/PD of the counterparty will increase Counterparty Risk and not EE ?Please correct me If am wrong here.

Basically I am trying to differentiate the definition of EE & Counterparty risk

Hope the question is more clear now

Thanks
Biju

But EE is based on counterparty risk, I don't think you can separate the 2 entirely.

If we enter a swap contract and in year 1 it's in my favor, then I incur the CCR because of +ve MTM hence +ve EE

If that reverses in year 2, then you incur the CCR because your EE is now +ve

 

[Biju]

Hi bpdulog,

Thanks.I understand that part of +ve MTM.

My question was that whether the EE figure depend on the Grade of a Counter party or not ?
Say for example if I have similar IRS (same contract terms) with two counter parties with Grade AA and BB.
After one year with same contract terms will I end up with same EE figure with both or different ?

I know CVA/Expected loss will be different .I am not getting clear on EE


Thanks
Biju

 

[Matthew Graves]

My understanding is that EE is as the name suggests, just the expected exposure amount. The only way this could be influenced by the credit-worthiness of the counter-party is if the PV of the position in question is related to the counter-party's credit rating. e.g. a CDS on the counter-party or a CDX where the counter-party is part of the bucket. Pretty unlikely to trade CDS with the CDS reference entity though for obvious reasons.

With reference to your IRS example, I would expect EE to be the same for both trades. CVA will of course be different.

 

[bpdulog]

My understanding is that EE is as the name suggests, just the expected exposure amount. The only way this could be influenced by the credit-worthiness of the counter-party is if the PV of the position in question is related to the counter-party's credit rating. e.g. a CDS on the counter-party or a CDX where the counter-party is part of the bucket. Pretty unlikely to trade CDS with the CDS reference entity though for obvious reasons.

With reference to your IRS example, I would expect EE to be the same for both trades. CVA will of course be different.

My intuition tell me that credit rating affects PD and not EE

 

[Matthew Graves]

Just to add, the venerable @David Harper CFA FRM makes a very good point about wrong-way risk. When you're taking into account wrong-way risk, the EE at time t is conditional on t being the time of default.

Thinking out loud here (happy to be corrected!), if the counter-party is more likely to default as the exposure gets higher and the EE(t | t = default) is the average exposure at time t given that t is the time of default then your average will be biased towards higher values as the lower exposure values are less likely to coincide with a default.

So...to summarise using your IRS example. If you ignore Wrong-Way Risk, then EE is unrelated to the counterparty credit rating and should be the same for both of your example counterparties. However, if you take a more accurate approach by accounting for wrong-way risk (i.e. correlation between exposure and default) and the correlation between PD and Exposure is not zero then EE will depend on the counterparty credit rating and the EE values will be different for the same instrument.

 

[FrmL2_Aspirant]

Just to add, the venerable @David Harper CFA FRM makes a very good point about wrong-way risk. When you're taking into account wrong-way risk, the EE at time t is conditional on t being the time of default.

Thinking out loud here (happy to be corrected!), if the counter-party is more likely to default as the exposure gets higher and the EE(t | t = default) is the average exposure at time t given that t is the time of default then your average will be biased towards higher values as the lower exposure values are less likely to coincide with a default.

So...to summarise using your IRS example. If you ignore Wrong-Way Risk, then EE is unrelated to the counterparty credit rating and should be the same for both of your example counterparties. However, if you take a more accurate approach by accounting for wrong-way risk (i.e. correlation between exposure and default) and the correlation between PD and Exposure is not zero then EE will depend on the counterparty credit rating and the EE values will be different for the same instrument.

crystal clear, very nicely explained ... pheww!!

 

[Biju]

Thanks everyone for clarifying this
Biju