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# Marginal CVA vs Incremental

#### kevinyuen

##### New Member
Subscriber
Hi all,

Can someone please help clarify the difference between Marginal CVA and Incremental CVA? I'm still a little confused about the difference between the two after reading the definitions a few times over.

Thanks.

#### zhukky

##### New Member
The concepts of marginal vs incremental are rather general, eg. can relate to VAR, CVA, etc.

Marginal refers to a change in a metric (eg. CVA) due to a (infinite)small change to a position (eg. Adding $1 or 1 share to existing position). Incremental refers to a conribution of a position as a whole to the metric (eg. CVA), for example the whole$10mln or all 500,000 shares. Incremental measures can be approximated via marginal ones.

#### afterworkguinness

##### Active Member
IMO this can be a confusing topic.
When a new position is priced, we want to know the value of the counterparty risk of the position and charge it to the client, as you know this is CVA. Assume we have other positions with this counterparty in a netting set; CVA will be expressed at the nettingset level. Perhaps it is a spread that we charge the counterparty every year.

We need to answer the question - "How much does this new trade change the CVA?". This question is answered by calculating the incremental CVA which is CVA with the trade included in the nettingset minus the CVA without the trade in the nettingset. That's great at time T when we price the trade, but the incremental CVAs are not additive - they don't sum up to the nettingset's CVA and it depends on the order of the trades.

If we want to breakdown the nettingset CVA and asses each trade's contribution to it, we want marginal CVA. Marginal CVA will tell us how much each trade contributes to the total CVA. Marginal CVAs are additive. BUT, there is a caveat. As we add new trades to the netting set, the marginal CVAs of all the existing trades change.

Marginal CVA is still good for assessing each trade's contribution to the overall nettingset CVA, but this means we cannot charge the counterparty the marginal CVA. Why? Since the marginal CVA of a trade depends on /changes the marginal CVA of all the other trades in the nettingset, the marginal CVA of the newly added trade may only account for part of the counterparty risk and the remaining fraction will never be charged to the client.

#### vijayaraghavan sundararajan

##### Member
Subscriber
Hello,

The concept of Marginal CVA or Incremental CVA can be explained from the point of view of exposure, i.e. marginal and incremental exposure.
The formula for CVA is (1-LGD) * Sum product of exposure*PD*Discount factor for various periods in future. Replacing the exposure with marginal and incremental exposure will lead to marginal and incremental CVA respectively.

Please refer the attachment Credit Exposure.xls, which will give an intuitive understanding behind the marginal and incremental exposure.

Rg
Vijay.

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#### nicoloco

##### New Member
That's great at time T when we price the trade, but the incremental CVAs are not additive - they don't sum up to the nettingset's CVA and it depends on the order of the trades.

Hi,

Is it really correct that the incremental are not additive ?
To me they are definitely additive by design and the marginal sum should equal the incremental sum,. The only problem is that it depends of the order of the trde, meaning that the first trade might have all the charge where a second might benefit from the neeting effect and get a small charge.
So the marginal is more a way to get rid of the trade order and look at your position at one point of time and answer the question : " so I have these position made up with these deal, which of these deals is contributing the most to my exposure ?"
It is just a fairer way to allocate the exposure ?

Am I missign something ?

cheers

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @nicoloco Gregory (assigned in T6) uses examples to illustrate the difference between marginal CVA and incremental CVA. There is a valid analogy to incremental (portfolio) VaR versus component VaR (which is a direct function of marginal VaR): just as component VaRs sum to portfolio VaR, marginal CVAs sum to total CVA and do not depend on the trade sequence. Incremental CVAs, however, do greatly depend on the trade sequence and do not sum to total CVA. From our question 418.3, both of the following statements are true:
• True: Incremental CVA depends on the order in which trades are executed but does not change due to subsequent trades. It makes the most sense when CVA needs to be charged to individual traders and businesses.
• True: Marginal CVA does change when new trades are executed. While it probably should not be used to price new transactions, it is good for pricing simultaneous transactions and to decompose a total CVA into its trade-level contributions
And Gregory:
"[Incremental CVA] makes the most sense when the CVA needs to be charged to individual traders and business. The [incremental] CVA depends on the order in which trades are executed but does not change due to subsequent trades. A CVA desk (Chapter 18) charging this amount will directly offset the impact on their PnL from the change in CVA from the new trade ...

Marginal CVA may be useful to break down a CVA for any number of netted trades into trade-level contributions that sum to the total CVA. Whilst it might not be used for pricing new transactions (due to the problem that marginal CVA changes when new trades are executed, implying PnL adjustment to trading books), it may be required for pricing trades transacted at the same time (perhaps due to being part of the same deal) with a given counterparty. Alternatively, marginal CVA is the appropriate way to calculate the trade-level CVA contributions at a given time. This may be useful where a CVA desk is concerned about their exposure to the default of a particular counterparty."

#### jbejarjimenez

##### New Member
Hi David,
Reading all of that, one simple question that is not 100% clear to me, CVA is performed for each trade of a counterpart (each trade of the counterpart will have different CVA) or for a counterpart itself (all trades with the counterpart will have the same CVA).
Regards

#### ijooma

##### New Member
Hi David

I have 2 questions.

What does the marginal CVA represent? I get the incremental is dependent on the EE of the next trade (please correct me if I am wrong). However I don’t get the marginal or how to derive the marginal cva. Please can you explain

Second question relates to table 14.6 in Greggory. On the incremental cva (5,4,3,2,1) why does the incremental cva on the 1st point not equal to the stand alone for the payer irs 5y (0.2587)

Thanks

Last edited by a moderator:

#### Nicole Seaman

Staff member
Subscriber
Hi David

I have 2 questions.

What does the marginal CVA represent? I get the incremental is dependent on the EE of the next trade (please correct me if I am wrong). However I don’t get the marginal or how to derive the marginal cva. Please can you explain

Second question relates to table 14.6 in Greggory. On the incremental cva (5,4,3,2,1) why does the incremental cva on the 1st point not equal to the stand alone for the payer irs 5y (0.2587)

Thanks
Hello @ijooma

I moved your question here to this thread, which already discusses marginal vs incremental CVA. I highly recommend our search function in the forum, which can save you a lot of time. Many times, you will find that your questions have already been answered

I also added Gregory's Table 14.6 to your post for reference, as it is much easier for David and other members to answer questions like this if the table you are referring to is shown.

Thank you,

Nicole

##### Member
Hi David,
Reading all of that, one simple question that is not 100% clear to me, CVA is performed for each trade of a counterpart (each trade of the counterpart will have different CVA) or for a counterpart itself (all trades with the counterpart will have the same CVA).
Regards
Hi @David Harper CFA FRM, I have the same doubt. Please advice.

Also, I want to know if below statement true

My calculated CVA (LGD of counterparty/PD of counterparty/my EE with the counterparty, for my counterparty) will be my counterparties DVA for itself?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Jaskarn Regarding the earlier doubt, that concerns most of Gregory's second half of his book. I do not have time for a long answer. Feel free to start a new discussion with other members. The short answer is that, certainly CVA is calculated at the trade (aka, position, instrument) level but also at the portfolio level.

re: My calculated CVA (LGD of counterparty/PD of counterparty/my EE with the counterparty, for my counterparty) will be my counterparties DVA for itself?

Yes, under Gregory's stated conditions of price-symmetry, this is true; e.g., obviously the counterparty's must agree on the respective exposures and PDs.