Marginal CVA

[Kavita.bhangdia]

David mentions in one of the problems that marginal CVA is greater than incremental CVA.

Why it is so.. I thought that incremental CVA will be large because you are adding an entire trade for CVAcalculation whereas marginal CVA is just a partial derivative..

Please clarify..

Thanks
Kavita

 

[ShaktiRathore]

Hi,
please visit following links if of any help:
https://forum.bionicturtle.com/threads/marginal-cva-vs-incremental.8772/#post-37655
I think Yes its theroretically possible that marginal CVA is greater than incremental CVA as was assumed by question/problem.Adding an entire trade does not mean you are adding the entire cva from the trade,the addition of trade should have non-additive effect on the overall CVA ,If new trade a is added than CVA(a+P)-CVA(P)(can be negative) is the resulting adition in CVA from trade can be anything <>=the marginal CVA, its not that you are adding the entire trade cva,marginal cva can be greater than incremental CVA.
thanks

 

[David Harper CFA FRM]

Thanks @ShaktiRathore !

@Kavita.bhangdia can you refer to the problem, please? ... because marginal CVA is not necessarily greater than incremental CVA. See Gregory's Table 12.6 below. Incremental CVA varies according to the sequence of trades (while marginal CVA does not suffer this issue) such that, you can see, marginal can be either less than or greater than incremental CVA.

For example, the cross currency swap has marginal CVA = 20,613 but its incremental CVA can be much larger (99,558) if it is the first trade or much smaller (5,822) if it is the last trade:

 

[David Harper CFA FRM]

@Kavita.bhangdia I think you may be referring to this question at https://forum.bionicturtle.com/thre...nd-marginal-credit-value-adjustment-cva.7254/ i.e.,

332.2. Each of the following is true about Marginal CVA except which is false?

a. By definition, Marginal CVA must be less than or equal to Incremental CVA
b. Unlike Incremental CVA, Marginal CVA is additive: the sum of Marginal CVAs is the total CVA
c. Marginal CVA is more relevant (than Incremental CVA) for apportioning CVA contributions fairly across existing trades or assessing the CVA of more than one new trade
d. Whereas it is difficult to price simultaneous trades with Incremental CVA, Marginal CVA is the appropriate way to calculate the trade-level CVA contributions of several trades at the same time

.... but I just used an example of marginal CVA greater than incremental CVA to show that (a) is false; I don't think I said that marginal CVA must be greater than incremental CVA. Thanks,

 

[Kavita.bhangdia]

Yes.. That is the question I was referring to.. Thanks David for clarification

Regards,
Kavita

 

[Arka Bose]

Hi @David Harper CFA FRM ,

If marginal CVA is additive, why does thetital of the last coloumn of marginal cva doesnt add up to the total of standalone cva?

 

[ami44]

Hi @David Harper CFA FRM ,

If marginal CVA is additive, why does thetital of the last coloumn of marginal cva doesnt add up to the total of standalone cva?

Because they add up to the netting-set cva, which is lower than the sum of the stand-alone cva. The netting-set cva is the actual cva and it includes diversification effects that are not present in stand-alone cva. The marginal cva is just a way to distribute the netzing-set cva back on the single deals, in some "fair" way.

By the way, I'm fairly certain that nobody uses the formula for marginal cva with the partial derivation in real live. What people do is, they distribute the netting-set cva according to the stand-alone cva of the deals. I believe, that often these two methods are the same, but not always.

 

[Arka Bose]

Hi @ami44 ,

Since I am reading this topic for the first time, things are still too cloudy. Apart from the incremental var being dependent on the sequence of trade, what does marginal cva on the other hand precisely do! Isnt both of the values dependedent on the extra amount of exposure added by a trade?

 

[Dr. Jayanthi Sankaran]

Hi @arkabose,

Please refer to the following link that Shakti Rathore has already referenced above:

https://forum.bionicturtle.com/threads/marginal-cva-vs-incremental.8772/#post-37655

They are excellent explanations given on the difference between incremental cva and marginal cva.

Thanks!

 

[David Harper CFA FRM]

Hi @ami44 In regard to to Gregory's Table 12.6 above, I would just add:

• On the total line, there is only a summation of standalone CVAs (392,973) which is maybe not so useful except as as unrealistic, undiversified CVA (but diversification here, just exactly as @ami44 says, is a dynamic really due to the netting agreement in the netting set) versus the "actual" (i.e., diversified at the netting set) total CVA of 257,905. Incremental and Marginal CVA do not really have meanings at the total level, as by definition, they refer to the CVA contribution of a trade (or number of trades) to the netting set.
• In terms of the four trades, Gregory only shows one Marginal CVA column because marginal CVA is additive and the trade sequence (within the netting set) does not matter; eg, Payer IRS GBP 57 would show the same 84,011 if it were 1st (1-2-3-4) or 4th (4-1-2-3). For each trade, sequence does impact incremental CVA, but while incremental CVA of the last trade (4th) varies, the total is the same netting-set CVA, to use @ami44 's language.
• In terms of these contribution dynamics, by analogy, marginal CVA is analogous to component VaR, while incremental CVA is analogous to incremental VaR. I hope that's helpful,