Marginal and Incremental CVA for Pricing New Trades
Summary
The document explains why marginal credit valuation adjustment (CVA) can help allocate a netting set’s total CVA across existing trades but can misstate the charge for a new transaction. Because each trade’s marginal CVA depends on the other trades in the netting set, adding a trade can change the allocated CVA of trades already booked. The discussion is conceptual and gives no numerical example.
Charging only the new trade’s marginal CVA may therefore recover less than the full increase in portfolio CVA: part of that increase is reassigned to existing trades and may never be billed to the client. Incremental CVA instead measures the full portfolio change from adding a trade, but its attribution depends on booking order. The document presents this as a trade-off between client pricing and assessing the current book; it does not describe a specific calculation procedure or address other pricing considerations.
Key ideas
- A trade’s marginal CVA depends on all trades in its netting set.
- Adding a trade can change the marginal CVA allocated to previously booked trades.
- Charging only the new trade’s marginal CVA may fail to recover the full increase in total CVA.
- Incremental CVA captures the full change from adding a trade, but its allocation depends on booking order.
- Marginal CVA can help assess existing portfolio contributions while being unsuitable as a standalone charge for a new trade.
Tags
Full text
# Why can't marginal CVA be used in pricing? # 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 ? ## Answer by AFK (score 1, accepted) https://quant.stackexchange.com/a/20917 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.