As regards your previous point, I am not sure I follow your meaning. I do agree that MtMs are additive, but I am afraid it’s not the point that you were making.

]]>Though I am a rookie in the world of quant finance, I would like to give some feedback on this,

It is true that PFE is non additive, but you forgot to mention PFE is time based profile and based on the same level of interest rates (simulated or stressed) at a particular time, the MTMs or the exposure ( from both side of the involved parties) can be used to cancelled out in a netted portfolio .

assumption : vanillas swaps portfolio only

Also can you give an intuitive explanation of a scenario when EPE profile can be over the PFE profile.

]]>Thanks for the non-subadditivity example, it’s a nice one.

Indeed, it’s naive to expect exposures to be additive, but I am surprised at how many people believe that the sum of the individual exposures is not very far off the total exposure. It takes a lot of effort to actually convince people that Monte Carlo is much better than just taking a PFE from a table, multiplying it by the notional, and adding up the results for all trades. People use some tricks to take netting into account, but those tricks were designed to work only under a few particular conditions. Naturally, no-one remembers anymore what those conditions were.

And yes, I do agree that tail exposure is a better measure than quantile.

]]>I didn’t know you had a blog.

While it is naive to expect exposures to be additive for the reasons you have exposed, I think it is reasonable to expect exposures to be subadditive, i.e., the exposure of 2 nettable trades together, can never be higher than the sum of the exposures of the 2 trades separately.

Quantiles don’t satisfy this property, you probably know the example. Consider a trade that pays 1 with probability 4% and 0 with probability 96%. It’s exposure (95% confidence) is zero.

Now consider 2 such trades. The sum of their exposures as separate trades is still zero. However, if you consider them as one whole (and assuming independence), you get:

with probability 0.96*0.96=92.16% it pays zero

with probability 2*0.96*0.04 = 7.68% it pays 1

with probability 0.04*0.04 = 0.16% it pays 2

The 95%ile is now 1.

I got this example from Richard’s paper on tail exposure as an example why quantiles are not a good measure of exposure.

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