# Why can't marginal CVA be used in pricing?

"Marginal CVA may be useful to breakdown 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 adjusting to trading books), it may be required for pricing trades transacted at the same time..." - John Gregory

Why would a marginal CVA change when a new trade is executed? I can see that the marginal CVA of a trade is time dependent, as the exposure of a trade changes so would its marginal CVA.

Putting aside that I don't understand how the marginal CVA wold change as a trade is added, why is this a problem for pricing the risk? A trader submits a transaction to the CVA desk for pricing of the risk so that it can be charged back to the counterparty, they come up with the value and voila done. What am I missing ?

The marginal CVA depends on every other trade in the netting set. This implies that adding a trade to the portfolio changes the marginal CVA of all the other existing trades in the portfolio.

Why is that problem? Imagine you only charge the client for the marginal CVA of each new trade. Since adding a new trade changes the CVA allocated to previously booked trades, the increase in total CVA will be dispatched among all the trades in the portfolio. So the marginal CVA of the new trade might represent only a fraction of the total increase in CVA and the remaining fraction will never be charged to the client. Note that the bank will still account for it because the total CVA is the sum of the marginal ones. So marginal CVA is good measure for the bank to know at a given date which trades are material to CVA but it is bad for knowing how much to charge for a new trade.

On the other hand, incremental CVA takes into account the full increase of CVA due to a new trade but the incremental CVA of each trade depends on the order they were booked which is not relevant when you want to assess the bank's books.

• Hi AFK, I do believe what you described is incremental CVA and not marginal. Sep 27, 2015 at 20:12
• Hi, the definition was indeed incorrect (I edited it) but the point remains: adding a trade changes the marginal cva of all the other trades in the netting set.
– AFK
Sep 27, 2015 at 20:21
• Can you expand on why it would be unfavorable for the marginal CVA to change with addition of new trades? Once the CVA is charged, what does it matter? Sep 27, 2015 at 20:29
• Expanded on marginal vs incremental CVA.
– AFK
Sep 27, 2015 at 21:15