In the previous post, we described the counterparty credit risk management and CVA concepts and discussed the OLAP cube. This post describes trade exposure in our CVA demo, using the Exposure and Potential Future Exposure (PFE) measures.
In counterparty credit risk management, the exposure of a trade at a given time point is the average of all the 1,000 exposure simulations.
The Potential Future Exposure (PFE) is the maximum exposure for a trade over its 20 time points. The PFE is the value that we show for the exposure measure in the cube when no time point is specified.
Although these counterparty credit risk management definitions are quite simple, it gets slightly more challenging when we need to aggregate these measures. In order to be able to aggregate them correctly, we will see that we first need to aggregate the simulation arrays in a certain way, and only then take the average of the resulting simulations to compute the aggregated exposure.
Indeed, the exposure of 2 trades at a given time point is the sum of these trades’ exposure if and only if they are part of the same netting node. If not, their combined exposure is the positive sum (or long sum) of their exposure.
exposure(a,b) = exposure(a)+ exposure(b) if a and b are in the same netting node
exposure(a,b) = max(exposure(a), 0) + max(exposure(b), 0) otherwise
For this reason, in order to compute the exposure of a set of trades for a given time point, we need to do a dynamic aggregation of their exposure arrays. For each netting node, the exposure arrays of their own trades are simply summed. Then, these resulting arrays (one per netting node) and the arrays of the non-netted trades (the trades that are not part of a netting node) are long summed, taking only the positive elements.
Finally, with the resulting exposure array, we can take the average of its 1,000 elements to compute the exposure for a given time point for this set of trades.
In the next post we will explain about the CVA netting concept, and about the CVA of a netting node.